In September 1997, Sean Carter raped and killed Veader Prince, his adoptive grandmother. State v. Carter , 89 Ohio St.3d 593 , 734 N.E.2d 345 , 347 (2000). Prior to trial, Carter's competency twice became a topic of controversy, leading to two hearings on the matter. Id. at 355-56 . Both times, Carter was deemed competent to stand trial. Ibid. Carter was subsequently found guilty of aggravated murder and of two capital specifications and was sentenced to death. Id. at 350 . Having exhausted his state-court appeals, Carter now brings this habeas corpus petition, alleging that he was incompetent at both the guilt and penalty phases of his trial and that his counsel were constitutionally ineffective. The district court denied the petition, Carter v. Bradshaw , No. 3:02CV524, 2015 WL 5752139 , at *1 (N.D. Ohio Sept. 30, 2015), and for the following reasons, we affirm.

I

A

In 1981, when he was 18 months old, Sean Carter ("Carter") was removed from his birth mother following a referral to a children service's agency in Trumbull County, Ohio. Carter , 734 N.E.2d at 347, 359 . When a caseworker investigated, she found Carter's mother-who suffered from schizophrenia-to be incoherent and Carter to be dirty, suffering from an enlarged *760 stomach, and tied by his ankle to the leg of a couch. Id. at 359 . After passing through several foster homes, Carter was eventually adopted by Evely Prince Carter when he was ten years old. Id. at 347, 359 . However, in February 1997, just shy of Carter's eighteenth birthday, Evely Prince Carter threw him out of her home, leading Carter to go live with her mother, Veader Prince ("Prince"). Id. at 347 . And there he stayed until his incarceration in July for theft. Ibid.

On September 13, 1997, Prince returned home to an unwelcome surprise. Unbeknownst to her, Carter had been released from jail and had let himself into her home. Id. at 347 . Upon discovering him, Prince directed her son, who was with her at the time, to give Carter the keys and title to his car; she then told Carter not to come back. Id. at 348-49 . The Supreme Court of Ohio summarized the subsequent events:

According to Carter's confession, after he obtained the car keys from [the victim's son], he left Prince's house and drove around for a while. He attempted to stay at his aunt's house, but could not. He returned to Prince's house and, since the door was locked, climbed through the bedroom window. He had called out to Prince, hoping to convince her to allow him to stay there for a week. They got into an argument and Prince told him to leave. He kept telling her that he had nowhere to go.

She tried to push him out the door and he started to beat her. At some point, he got a knife from the kitchen and started stabbing her. He described it as just "going off" and could not provide exact details of what happened during the assault, although he did remember hitting her in the face and stabbing her in the neck.

The next thing Carter remembered was being in the kitchen and washing his hands and the knife. He walked downstairs and saw Prince on the basement floor and then started to cover things up. He covered her with some clothes, moved the couch in her bedroom to cover up blood on the carpet, turned the water on in her bathroom and closed the door, and put a chicken in a pot on the stove and turned the stove on. He left a note on the kitchen table saying, "Took Sean to the hospital" in case someone saw blood in the house. He changed his clothes, since they were bloody. He then took about $150 from her purse and left.

He originally took her keys, thinking he would take one of her vans, and actually put his bag of clothes in the van, but could not get the van started. He got into [the victim's son's] car and drove off. Since he did not have a license plate, he stopped to steal a plate from a car in Garrettsville. To remove and transfer the plates to his car, he used the knife that he had stabbed his grandmother with.

Id. at 349-50 .

Late in the evening of September 14, Prince's body was discovered by her children. Id. at 348 . An autopsy revealed that she had been stabbed 18 times, had suffered blunt-force trauma to the head, and had been anally raped. Id. at 349 . Semen found in the victim's anus was later positively identified as Carter's. Id. at 353 .

The next day, Carter was detained by police in Beaver County, Pennsylvania, and, after being given his Miranda warnings, he confessed to Prince's murder. Id. at 349 . He was subsequently extradited to Ohio, where he was indicted for, inter alia , one count of aggravated murder with three capital specifications, namely, aggravated burglary, aggravated robbery, and rape. Id. at 350 .

Prior to trial, a competency hearing was held at the request of defense counsel.

*761 Because Carter had attempted to commit suicide "several" times while in custody, his arms and legs were shackled throughout the proceedings, and he was guarded by three members of the Trumbull County Sheriff's Department. Despite these circumstances, the court concluded that Carter was competent to stand trial based upon the testimony of Dr. Stanley Palumbo, a court-appointed licensed psychologist. Id. at 355 . According to Palumbo,

[w]ith reasonable scientific certainty[,] Mr. Carter [was] competent to stand trial. Mr. Carter underst[ood] the nature of the proceedings against him and d[id] not suffer from any gross mental disorder that would [have] interfere[d] with his ability to participate in his defense. He d[id] not suffer from any mood disorder such as depression, which would [have] cause[d] him to have trouble following a witness's line of statements or [not] have the energy and interest in participating in his own defense in his own best interest.

Ibid. In its findings of fact, the court further noted that while "Palumbo testified that the Defendant does not trust his attorney, or any other attorney ... Defendant's distrust of his attorney does not exhibit paranoid behavior since he distrusts all attorneys and not specifically his attorney." Ibid.

Shortly thereafter, Carter entered a plea of not guilty by reason of insanity. Ibid. In advance of the trial, the defense hired Dr. Steven A. King to assess Carter's mental state at the time of the crime. While interviewing Carter, King became concerned that Carter was not competent to stand trial based upon "several subtle signs of a psychotic disorder"-such as inappropriate laughter and auditory and visual hallucinations-as well as Carter's musing about killing Anthony Consoldane, one of his trial counsel. Following a motion by Carter's counsel, a second competency hearing was held on February 26, 1998.

At the hearing, three experts-King, Palumbo, and forensic psychiatrist Dr. Robert Alcorn-testified. Id. at 355-56 . While King reiterated his diagnosis that Carter was incompetent-specifically, due to "his paranoia, his hostility and his inability to cooperate in his defense"-he acknowledged that "this was a close call, this is a subtle case." 1 Palumbo and Alcorn, however, disagreed. Palumbo, who had examined Carter on four different occasions, testified that Carter understood the charges against him, at no time seemed to be responding to auditory or visual hallucinations, and did not demonstrate confusion or agitation. Palumbo further attributed Carter's anger towards his attorneys to personality issues and to "questions about his attorneys proceeding for him on his behalf." Alcorn echoed Palumbo's assessment, opining that Carter was aware of the nature of the proceedings against him, that Carter had attempted to feign signs of mental illness during one of his interviews, and that Carter's antipathy towards Attorney Consoldane was related to Carter's assessment of Consoldane's performance. At the conclusion of the hearing, the trial court once again found Carter competent to stand trial, noting that even King had acknowledged that the issue was borderline and that a defendant's distrust of or hostility towards his attorney does not necessarily equate with incompetence. Id. at 356 .

*762 Two weeks later, during the trial's opening statements, Carter interrupted defense counsel to express his desire to plead guilty. After the statements concluded, a brief recess was held, at which time Carter informed the court that he did not wish to attend the proceedings. Initially, the trial judge stated that he would hold off on deciding that matter, as he wished to research the issue to ensure that Carter's rights were adequately protected. Carter was, however, insistent that he did not want to attend the trial; and after asking whether he would be removed if he "acted up" in court, he lunged at the judge. The court described the ensuing events:

[w]hat happened is basically the Defendant lost complete control, indicated to the Court that he would act up and, in fact, proceeded to jump around, went crazy causing the deputies, four deputies to restrain him and put him in leg irons. And he struggled very violently with them. And he has promised to the Court that he intends to continue that type of activity throughout the trial if he's required to be here.

Defense counsel agreed with this characterization of the incident and stipulated that until Carter could control himself, Carter would monitor the proceedings via television in a separate room. The trial judge then directed defense counsel to inform the court if Carter changed his mind about attending the proceedings.

On March 20, 1998, Carter was convicted of one count of aggravated murder and of two capital specifications, namely, that the murder was committed in connection with rape and in connection with aggravated robbery. Id. at 350 . Following a penalty hearing, the jury recommended a sentence of death; and on April 2, 1998, the trial court adopted the jury's recommendation. 2 Ibid.

Represented by new counsel, Carter immediately appealed his conviction and sentence, raising fourteen propositions of law; for purposes of this appeal, however, only two are relevant.

Proposition of Law No. 4

U.S. Const. amend. XIV and Ohio Const. art. I, §§ 1, 2, and 16, require [the] trial court, when presented with bona fide evidence and good faith claims that a criminal defendant is incompetent to stand trial, to examine all reasonably available evidence.

Proposition of Law No. 5

Ineffective assistance of counsel violates not only a capital defendant's rights to effective counsel under U.S. Const. amend. VI and XIV[,] and Ohio Const. art. I, §§ 1 and 10 ; but also rights to a fair and impartial jury trial and a reliably determined sentence, as guaranteed by [ ] U.S. Const. amend.[ ] V, VI, VIII, and XIV and by Ohio Const.[ ] art. I, §§ 5, 9, 10, and 16.

Carter , 2015 WL 5752139 , at *5 (alterations in original). As part of the latter proposition of law, Carter argued that trial counsel were constitutionally ineffective because they failed to accept the trial court's offer of MRI testing for Carter.

On September 13, 2000, the Supreme Court of Ohio affirmed Carter's conviction and death sentence. Carter , 734 N.E.2d at 350 . With respect to the former proposition of law, the court noted that Carter's argument focused solely on his alleged inability to assist counsel during the proceedings. Id. at 355 . After a careful review of *763 the record-during which it emphasized that two experts had found Carter to be competent, while the third had characterized the issue as a "close call"-the court concluded that "[t]he trial court's findings of fact fail to support Carter's claim that the court's [competency] decision was unreasonable, arbitrary, or unconscionable." Id. at 356 . As regards Carter's ineffective-assistance-of-counsel claims, the Supreme Court of Ohio held that they were "speculative" given the record. Id. at 356-57 . For instance, concerning Carter's claim regarding the failure to pursue MRI testing, the court noted that there was no way to know whether Carter had been prejudiced by counsels' decision absent the forgone MRI; and because the claim required extrarecord evidence, it could "not appropriately [be] considered on direct appeal" under Ohio law. Id. at 357 .

B. State-Court Postconviction Proceedings

While his direct appeal was pending, Carter also filed a "petition to vacate or set aside conviction," which the trial court interpreted as a petition for postconviction relief. State v. Carter , No. 99-T-0133, 2000 Ohio App. LEXIS 5935, at *2 (Ohio Ct. App. Dec. 15, 2000). In relevant part, Carter raised the following causes of action:

SECOND CAUSE OF ACTION

Petitioner was incompetent to stand trial because his paranoid personality did not permit him to trust his lawyers. He therefore could not and did not work cooperatively with counsel, a basic component of competence to stand trial. Further, counsel was physically afraid of Petitioner, which resulted in a diminution of the attorney-client relationship, and counsel failed to present out of court evidence by an expert witness who acknowledged that counsel could not possibly have an effective working relationship with Petitioner.

...

Petitioner's trial counsel failed to (a) present all evidence of Petitioner's incompetence; (b) make a complete record on Petitioner's behalf so that Petitioner could defend his life and liberty on appeal if convicted; and (c) present, through direct or cross examination, all expert evidence of Petitioner's incompetence to stand trial.

FIFTH CAUSE OF ACTION

Petitioner's trial counsel violated the duty to conduct [an investigation of possible mitigating factors] by:

(A)failing to fully investigate Petitioner's medical and social history; and

(B) failing to hire a mitigation expert to assist in discovery of relevant information.

On August 30, 1999, the trial court dismissed the petition without a hearing, finding that Carter "ha[d] failed to show substantive grounds for relief as to any of the claims set forth" therein. See ibid. Specifically, the court held that the aforementioned causes of action were barred by the doctrine of res judicata, as the issues had been or could have been raised before the Supreme Court of Ohio on direct appeal. In the alternative, the court found that dismissal of the claims without a hearing was warranted because Carter had failed to "submit[ ] evidentiary documents which contain sufficient facts to demonstrate the denial of a constitutional right and resultant prejudice[.]"

On September 29, 1999, Carter appealed the postconviction trial court's decision, alleging two errors.

Assignment of Error No. 1

The trial court erred in denying appellant an evidentiary hearing on his petition for post-conviction relief, thus depriving appellant of liberties secured by U.S. Const. amend. VI and XIV, and Ohio Const. art. I [§§] 1, 2, 10, and 16, *764 including meaningful access to the courts of this State.

Assignment of Error No. 2

The trial court erred in applying the principles of res judicata , thus depriving appellant of liberties secured by U.S. Const. amend. VI and XIV, and Ohio Const. art. I, [§§] 1, 2, 10, and 16.

Id. at *2-3. On December 15, 2000, the Court of Appeals of Ohio affirmed the judgment of the trial court, holding that the first assignment of error was "without merit" and, therefore, that the second one was moot. Id. at *13. In doing so, the court noted that (1) it did not appear that Carter's counsel performed inadequately during the mitigation phase of the trial and (2) Carter had not submitted evidentiary documents that would have entitled him to a hearing on his claim of ineffective assistance of counsel during the mitigation phase. Id. at *10, 13. Once again, Carter appealed the decision, 3 but on May 2, 2001, the Supreme Court of Ohio declined jurisdiction and dismissed the case as not involving any substantial constitutional question. State v. Carter , 91 Ohio St.3d 1509 , 746 N.E.2d 612 (Ohio 2001) (Table).

Nearly one-and-three-quarters years later, Carter filed an application with the Supreme Court of Ohio to reopen his direct appeal on the grounds that he had been denied effective assistance of appellate counsel. In particular, Carter alleged that appellate counsel had failed to raise "all instances of prosecutorial misconduct and ineffective assistance of [trial] counsel, and the failure of the trial court to ensure that Mr. Carter was competent to stand trial and to safeguard his right to be present." On March 19, 2003, the court denied the application without discussion. State v. Carter , 98 Ohio St.3d 1486 , 785 N.E.2d 470 (Ohio 2003) (Table).

C. Federal Habeas Corpus Proceedings

In March 2002, prior to Carter's filing an application to reopen his direct appeal, the Office of the Ohio Public Defender ("OPD") initiated habeas corpus proceedings on the Petitioner's behalf by filing a suggestion of incompetence. In its application, the OPD noted that Carter-who, at that time, may have waived further review of his case and have volunteered for execution-was then being held at a facility for inmates with severe mental illness and that his case worker had said that Carter was mentally ill. Because Carter was not represented by counsel and had refused to meet with the office's representatives, the OPD simultaneously filed a motion for the appointment of counsel and an ex parte motion for the appointment of a mental-health expert to determine whether Carter was competent to waive federal review of his conviction and death sentence. The district court granted the motions, and on May 1, 2002, habeas counsel filed a petition for a writ of habeas corpus, pursuant to 28 U.S.C. § 2254 , on Carter's behalf. In July 2002, counsel withdrew OPD's ex parte request after Carter met with them and stated that he wanted to pursue his case in federal court with their representation.

Carter, who amended his petition three times between May 2002 and October 2005, raised nine claims on habeas review.

GROUND FOR RELIEF ONE

*765 Sean Carter was incompetent at both the culpability and penalty phases of his trial. Therefore, his convictions and sentence of death are in violation of his rights under the Fifth, Sixth, Eighth, and Fourteenth Amendments to the United States Constitution.

GROUND FOR RELIEF TWO

Sean Carter's right to effective assistance of counsel during the mitigation phase was violated when counsel failed to investigate, prepare, and present relevant mitigating evidence. U.S. Const. amend[ ]. VI, VIII, XIV.

GROUND FOR RELIEF THREE

Sean Carter's rights to a fair trial and an impartial jury were violated by prosecutor misconduct at the culpability phase of Mr. Carter's trial. U.S. Const. amend. VI and XIV.

GROUND FOR RELIEF FOUR

The trial court denied Sean Carter his rights under the Fifth, Sixth, Eighth, and Fourteenth Amendments to the United States Constitution by failing to instruct the jury properly at the conclusion of the culpability phase.

GROUND FOR RELIEF FIVE

Sean Carter was denied his right to the effective assistance of counsel under the Sixth and Fourteenth Amendments to the United States Constitution when his attorneys failed to object and properly preserve numerous errors that occurred during the pre-trial proceedings and the culpability phase of the trial.

GROUND FOR RELIEF SIX

Sean Carter was denied the effective assistance of counsel in his direct appeal as of right, in violation of his rights under the Fifth, Sixth, Eighth and Fourteenth Amendments to the United States Constitution.

GROUND FOR RELIEF SEVEN

The death penalty as administered by lethal injection in the state of Ohio violates Sean Carter's rights to protection from cruel and unusual punishment and to due process of law as guaranteed by the United States Constitution amend [ ]. VIII and XIV.

GROUND FOR RELIEF EIGHT

Sean Carter is seriously mentally ill. Therefore, his death sentence is in violation of his rights under the Eighth and Fourteenth Amendments.

GROUND FOR RELIEF NINE

Sean Carter will not be competent and sane to be executed. Sean's execution while he is incompetent and insane, violates the Eighth and Fourteenth Amendments to the United States Constitution.

Carter , 2015 WL 5752139 , at *10 (alterations in original). On the same day that Carter filed his third amended petition, he also filed a motion to expand the record and moved for a competency determination and to stay the proceedings.

In late November 2005, the district court granted Carter's motion for a competency determination, and granted in part and denied in part his motion to expand the record. Of particular note, the court refused to expand the record to include (1) an affidavit from Ida Magee, who served as Carter's foster mother prior to his adoption by Evely Prince Carter, (2) a psychosocial history of Carter prepared by Albert Linder, a psychiatric social worker, (3) a letter from psychologist Dr. Douglas Darnall that detailed Carter's mental illness, (4) an April 1994 chemical-dependency assessment of Carter by the Portage County Juvenile Court, and (5) a March 1995 Department of Youth Services evaluation. The court's refusal was based on the grounds that Carter had not been diligent in presenting that evidence to the Ohio courts. See 28 U.S.C. § 2254 (e)(2).

Five months later, on May 1, 2006, the district court finally conducted a hearing to determine whether Carter was competent *766 to proceed with his habeas petition. The next day, the court ordered Carter's counsel to arrange for both parties' experts to observe habeas counsels' interactions with Carter, presumably to assess his purported "inability to communicate with counsel in a meaningful way concerning the facts and issues in his case." After the court denied Carter's objection to the order-specifically, that it threatened to violate his attorney-client privilege-he sought a Certificate of Appealability ("COA"), pursuant to 28 U.S.C. § 1292 (b). And although the district court also denied Carter's motion to certify the appeal, it granted his request to stay discovery pending a resolution of the issue by the Sixth Circuit. In November 2007, we granted Carter's request for mandamus relief and set aside the district court's order.

In September 2008, nearly three years after Carter filed his motion for a competency determination, the district court held that the Petitioner was incompetent to proceed with his federal habeas litigation. Carter v. Bradshaw , 583 F.Supp.2d 872 , 873 (N.D. Ohio 2008), vacated , 644 F.3d 329 (6th Cir. 2011), rev'd Ryan v. Gonzales , 568 U.S. 57 , 133 S.Ct. 696 , 184 L.Ed.2d 528 (2013). According to the district court, Carter was incompetent because he was unable to assist habeas counsel in developing the removal-from-trial, competency, and ineffective-assistance-of-counsel claims that were raised in his petition. The court based this finding on its determination that Carter:

could not reasonably be expected to recall and describe how well he was able to view the trial once he was removed from it ..., [ ] would be unable to elaborate on conversations he had with defense counsel regarding his competency ... [, and] does not have the present capability to judge and express to habeas counsel what mitigating evidence from his social and family background defense counsel should have introduced during the sentencing phase of trial because of his limited capacity to recall and convey the details about any such events.

Carter , 583 F.Supp.2d at 882 . 4 The court accordingly dismissed the case without prejudice and prospectively tolled the one-year statute of limitations set forth in 28 U.S.C. § 2244 (d). Id. at 884-85 .

On appeal, a panel of this court amended the district court's judgment, directing that Carter's habeas proceedings be stayed with respect to those claims for which Carter's assistance was "essential." Carter , 644 F.3d at 337 . It did so on the grounds that pursuant to 18 U.S.C. § 4241 , federal habeas petitioners facing the death penalty for state criminal convictions have a statutory right to competence. Ibid. The Supreme Court subsequently granted certiorari "to determine whether § 4241 provide[d] a statutory right to competence in federal habeas proceedings." Gonzales , 568 U.S. at 64 , 133 S.Ct. 696 .

On January 8, 2013, the Supreme Court unanimously vacated the judgment of the Sixth Circuit. Gonzales , 568 U.S. at 77 , 133 S.Ct. 696 . In so doing, the Court also addressed Carter's argument that the stay was a proper exercise of the Northern District of Ohio's "equitable power to stay proceedings when [it] determine[s] that habeas petitioners are mentally incompetent." Id. at 73 , 133 S.Ct. 696 . "For purposes of resolving the[ ] case[ ]," the Court noted that Carter's first, second, and fifth habeas claims had been "adjudicated on the merits in state postconviction proceedings and, thus, were subject to review *767 under [ 28 U.S.C.] § 2254(d)." Id. at 74, 75 , 75 n.15-16, 133 S.Ct. 696 . Accordingly, the Court concluded that these claims did not warrant a stay because "[a]ny extrarecord evidence that Carter might have concerning [them] would be ... inadmissible." Id. at 75 , 133 S.Ct. 696 (citing Cullen v. Pinholster , 563 U.S. 170 , 181, 131 S.Ct. 1388 , 179 L.Ed.2d 557 (2011) ).

Upon remand, the district court denied Carter's petition for a writ of habeas corpus. Carter , 2015 WL 5752139 , at *1. Having done so, the court then issued a COA as to Carter's: (1) "First ground for relief regarding his competency to stand trial," (2) "Second ground for relief relating to his trial counsel's ineffective assistance during the mitigation phase of trial," and (3) "Fifth ground for relief relating to his trial counsel's ineffective assistance regarding his competency to stand trial." Id. at *52. We subsequently denied Carter's application to expand the COA and his request that we order both a competency evaluation and a limited stay in the proceedings. Accordingly, only the aforementioned three issues are before this court. See 28 U.S.C. § 2253 (c).

II

When reviewing a district court's grant or denial of a petition for a writ of habeas corpus, we examine its conclusions of law de novo and its factual findings for clear error. Hand v. Houk , 871 F.3d 390 , 406 (6th Cir. 2017). Additionally, because Carter filed his habeas petition after 1996, the scope of our review is further restricted by the Antiterrorism and Effective Death Penalty Act ("AEDPA"), Stojetz v. Ishee , 892 F.3d 175 , 190 (6th Cir. 2018), which was designed to "prevent federal habeas 'retrials' and to ensure that state-court convictions are given effect to the extent possible under law[,]" Bell v. Cone , 535 U.S. 685 , 693, 122 S.Ct. 1843 , 152 L.Ed.2d 914 (2002).

Among other things, AEDPA limits the circumstances under which we may grant a writ of habeas corpus with respect to any claim that was adjudicated on the merits in a state court. See 28 U.S.C. § 2254 (d). More specifically, under AEDPA, we may grant a writ only if the state court's adjudication of the claim:

(1) resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States; or

(2) resulted in a decision that was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.

Ibid. A state court's adjudication of a claim is "contrary to" clearly established federal law "if the state court arrives at a conclusion opposite to that reached by the Supreme Court on a question of law, or if the state court decides a case differently than the Supreme Court on a set of materially indistinguishable facts." Stojetz , 892 F.3d at 192 (quoting Van Tran v. Colson , 764 F.3d 594 , 604 (6th Cir. 2014) ). In contrast, an "unreasonable application" of clearly established federal law occurs where "the state court identifies the correct governing legal principle from [the Supreme] Court's decisions but unreasonably applies that principle to the facts of the [petitioner's] case." Williams v. Taylor , 529 U.S. 362 , 413, 120 S.Ct. 1495 , 146 L.Ed.2d 389 (2000). For purposes of AEDPA, "clearly established federal law" only "refers to the holdings, as opposed to the dicta, of [the Supreme] Court's decisions as of the time of the relevant state-court decision." Lockyer v. Andrade , 538 U.S. 63 , 71, 123 S.Ct. 1166 , 155 L.Ed.2d 144 (2003) (quoting Williams , 529 U.S. at 412 , 120 S.Ct. 1495 ).

To be clear, "an unreasonable application of federal law is different from *768 an incorrect application of federal law." Renico v. Lett , 559 U.S. 766 , 773, 130 S.Ct. 1855 , 176 L.Ed.2d 678 (2010) (quoting Williams , 529 U.S. at 410 , 120 S.Ct. 1495 ). Stated more bluntly, under the "unreasonable application" clause of § 2254(d)(1), it does not matter whether a federal habeas court might "conclude[ ] in its independent judgment that the [state court] applied clearly established federal law erroneously or incorrectly[.]" Gagne v. Booker , 680 F.3d 493 , 513 (6th Cir. 2012) (en banc) (first two alterations in original) (quoting Williams , 529 U.S. at 411 , 120 S.Ct. 1495 ). Rather, a federal habeas court may issue the writ pursuant to this clause only where the relevant state-court decision applied clearly established federal law in an objectively unreasonable manner, Lett , 559 U.S. at 773 , 130 S.Ct. 1855 , i.e., only where "the state court's ruling ... was so lacking in justification that there was an error well understood and comprehended in existing law beyond any possibility for fairminded disagreement[,]" Harrington v. Richter , 562 U.S. 86 , 103, 131 S.Ct. 770 , 178 L.Ed.2d 624 (2011).

Review under § 2254(d)(1) is limited in two additional, important ways. First, notwithstanding the language of 28 U.S.C. § 2254 (e)(2), review is restricted to the record that was before the court that adjudicated the claim on the merits. Pinholster , 563 U.S. at 181, 184 , 131 S.Ct. 1388 . Second, when determining whether the "unreasonable application" standard is met, courts must consider the rule's specificity; that is because "the range of reasonable judgment can depend in part on the nature of the relevant rule." Yarborough v. Alvarado , 541 U.S. 652 , 664, 124 S.Ct. 2140 , 158 L.Ed.2d 938 (2004). "The more general the rule, the more leeway courts have in reaching outcomes in case-by-case determinations." Ibid.

As regards 28 U.S.C § 2254(d)(2), it too imposes a highly deferential standard when reviewing claims of factual error by a state court. See Burt v. Titlow , 571 U.S. 12 , 18, 134 S.Ct. 10 , 187 L.Ed.2d 348 (2013). The Supreme Court has been clear that "a state-court factual determination is not unreasonable merely because the federal habeas court would have reached a different conclusion in the first instance." Ibid. (quoting Wood v. Allen , 558 U.S. 290 , 301, 130 S.Ct. 841 , 175 L.Ed.2d 738 (2010) ). Stated differently, it is not enough that reasonable minds reviewing the record might disagree with the state court's factual determination; rather, the record must " compel the conclusion that the [state] court had no permissible alternative" but to arrive at the contrary conclusion. Rice v. Collins , 546 U.S. 333 , 341-42, 126 S.Ct. 969 , 163 L.Ed.2d 824 (2006) (emphasis added). Equally important, "it is not enough for the petitioner to show some unreasonable determination of fact; [additionally], the petitioner must show that the resulting state court decision was 'based on' that unreasonable determination." Rice v. White , 660 F.3d 242 , 250 (6th Cir. 2011) (emphasis added). 5

III

A

It is well-established that "the criminal trial of an incompetent defendant *769 violates due process." Cooper v. Oklahoma , 517 U.S. 348 , 354, 116 S.Ct. 1373 , 134 L.Ed.2d 498 (1996) (quoting Medina v. California , 505 U.S. 437 , 453, 112 S.Ct. 2572 , 120 L.Ed.2d 353 (1992) ); see also Drope v. Missouri , 420 U.S. 162 , 171, 95 S.Ct. 896 , 43 L.Ed.2d 103 (1975). It is equally well-established that one who lacks either a "sufficient present ability to consult with his lawyer with a reasonable degree of rational understanding" or "a rational as well as factual understanding of the proceedings against him" is not competent to stand trial. Dusky v. United States , 362 U.S. 402 , 402, 80 S.Ct. 788 , 4 L.Ed.2d 824 (1960) (per curiam). Accordingly, where there is substantial doubt as to a defendant's "capacity to understand the nature and object of the proceedings against him, to consult with counsel, and to assist in preparing his defense[,]" Drope , 420 U.S. at 171 , 95 S.Ct. 896 , a trial court "must sua sponte order an evidentiary hearing on the ... issue[,]" Williams v. Bordenkircher , 696 F.2d 464 , 466 (6th Cir. 1983) (citing Pate v. Robinson , 383 U.S. 375 , 385, 86 S.Ct. 836 , 15 L.Ed.2d 815 (1966) ).

While the Supreme Court has yet to prescribe a standard for determining when a trial court should hold evidentiary proceedings on the matter of competency, we have previously used the following test: "whether a reasonable judge, situated as was the trial court judge whose failure to conduct an evidentiary hearing is being reviewed, should have experienced doubt with respect to competency to stand trial." Filiaggi v. Bagley , 445 F.3d 851 , 858 (6th Cir. 2006) (quoting Williams , 696 F.2d at 467 ). "[E]vidence of a defendant's irrational behavior, his demeanor at trial, and any prior medical opinion on competence to stand trial are all relevant in determining whether further inquiry is required, but ... even one of these factors standing alone may, in some circumstances, be sufficient." Black v. Bell , 664 F.3d 81 , 102 (6th Cir. 2011) (alterations in original) (quoting Drope , 420 U.S. at 180 , 95 S.Ct. 896 ). Where, however, a trial court has already held a competency hearing and deemed the defendant competent, it need not reevaluate its determination unless presented with qualitatively different evidence. See Franklin v. Bradshaw , 695 F.3d 439 , 450 (6th Cir. 2012).

Because competence to stand trial is a question of fact, see Thompson v. Keohane , 516 U.S. 99 , 111, 116 S.Ct. 457 , 133 L.Ed.2d 383 (1995), and because Ohio law incorporates the Drope standard for competency, see O.R.C. § 2945.37(G), 6 a petitioner challenging an Ohio court's finding of competence is subject, at minimum, 7 to the strictures of 28 U.S.C. § 2254 (d)(2), see Filiaggi , 445 F.3d at 858-59 (reviewing Supreme Court of Ohio's competency determination, *770 which was made pursuant to Ohio law, under 28 U.S.C. § 2254 (d)(2) and (e)(1) ); see also Black , 664 F.3d at 102 (stating that a state court's competency-to-stand-trial determination is entitled to deference under 28 U.S.C. § 2254 (e)(1) provided that "the state court's legal standard for determining whether a defendant is competent is not contrary to or an unreasonable application of clearly established Supreme Court precedent"). In other words, not only must a petitioner show that the state court's determination was unreasonable, but he may not draw upon any extrarecord evidence to make his argument. See Pinholster , 563 U.S. at 185 , 131 S.Ct. 1388 . When assessing whether a petitioner has met this burden, it is important to keep in mind "that a state-court factual determination is not unreasonable merely because the federal habeas court would have reached a different conclusion in the first instance." Titlow , 571 U.S. at 18 , 134 S.Ct. 10 (quoting Wood , 558 U.S. at 301 , 130 S.Ct. 841 ).

B

Although Carter frames his first cause of action as a single claim-namely, that he was incompetent at both the guilt and penalty phases of the trial-it actually consists of two analytically distinct parts. In his first subclaim, Carter raises a question of fact. Specifically, he asserts that "the trial court's [and the Supreme Court of Ohio's] determination of Carter's competency was unreasonable based upon the evidence available at the state court proceeding[,]" both because the courts either ignored or misinterpreted relevant evidence and because they credited flawed expert testimony. Petitioner Br. 22, 27, 31. Carter supports this subclaim, at least in part, by pointing to the following evidence, which he contends the state courts overlooked or did not properly credit: his family history of schizophrenia, his hallucinations as a juvenile and during his competency evaluations, his attempts at suicide while in state custody, his expressed desire to kill one of his trial attorneys, his purported lack of understanding of the role of trial counsel, and his desire to receive the death penalty. Id. at 22-26.

In contrast, Carter's second subclaim-i.e., that even if the trial court's initial determination was not unreasonable, evidence that arose after the competency hearings should have led the court to reevaluate its finding, id. at 32-is an issue of law, see Hill v. Anderson , 881 F.3d 483 , 510-11 (6th Cir. 2018) (assessing a petitioner's failure-to-hold-a-competency-hearing claim pursuant to 28 U.S.C. § 2254 (d)(1) ); see also Franklin , 695 F.3d at 450 ("[T]he trial court's failure to hold a midtrial competency hearing sua sponte was not a 'decision that was contrary to, or involved an unreasonable application of, clearly established Federal law.' " (citing 28 U.S.C. § 2254 (d)(1) ) ). But see id. at 451 (indicating later that failure-to-hold-a- sua - sponte -competency-hearing claim is subject to review pursuant to 28 U.S.C. § 2254 (d)(2) ). Specifically, Carter cites his outbursts in court-most notably, his interrupting defense counsel's opening statement to express his desire to plead guilty and his subsequent attempt to assault the trial judge-as evidence that the trial court should have revisited the finding it made at the second competency hearing. Petitioner Br. 25, 32.

As already detailed, Carter raised this competency claim on direct appeal, where it was adjudicated on the merits. Carter , 734 N.E.2d at 355-56 . With respect to Carter's first subclaim, the Supreme Court of Ohio acknowledged that the record contained some indications of Carter's being incompetent, but emphasized that such evidence was insufficient to overcome the opinions of the expert witnesses, two of whom testified that Carter was competent *771 to stand trial and the third of whom "admitted that the question of competence was a close call." Ibid. The court accordingly held that the trial court did not abuse its discretion in finding Carter competent because that decision was not "unreasonable, arbitrary, or unconscionable" in light of the findings of fact. Id. at 356 . As regards the denial of Carter's second subclaim, the Supreme Court of Ohio did not explicitly discuss it; nevertheless, that too qualifies as an adjudication on the merits for the purposes of 28 U.S.C. § 2254 (d). See Richter , 562 U.S. at 98 , 131 S.Ct. 770 ("By its terms § 2254(d) bars relitigation of any claim 'adjudicated on the merits' in state court, subject only to the exceptions in §§ 2254(d)(1) and (2). There is no text in the statute requiring a statement of reasons.").

C

As a preliminary matter, it is simply not true that the Supreme Court of Ohio failed to consider the host of evidence that Carter points to. In arriving at its conclusion that the trial court's findings of fact did not support Carter's competency claim, the Supreme Court of Ohio explicitly recognized Carter's suicide attempts while awaiting trial, his "apparent disagreements with counsel[,]" his desire to "enter a plea and get it over[,]" and his "lung[ing] at the judge to be removed from the courtroom." Carter , 734 N.E.2d at 356 , 356 n.3. Furthermore, while discussing the expert witnesses' testimony, the court noted Carter's "anger and irritability with his attorneys," including his having expressed a desire to kill Consoldane, as well as his "bizarre behavior"-presumably, his auditory and visual hallucinations-during his competency interview with Dr. King. Id. at 355-56 . At most, then, the court can be faulted for a relatively minor oversight, namely, not explicitly considering Carter's family history of mental illness.

i

Turning now to Carter's first subclaim, the Supreme Court of Ohio's decision affirming the trial court's competency determination was not unreasonable in light of the evidence presented in state court. At Carter's second competency hearing, Drs. Palumbo and Alcorn testified that Carter was competent to stand trial, while Dr. King-who testified that Carter was incompetent-described the issue as a "close call." 8 Given that, all else equal, it is not unreasonable for a court to credit the diagnoses of two experts over that of a third (especially when that contrary opinion is heavily qualified), see O'Neal v. Bagley , 743 F.3d 1010 , 1023 (6th Cir. 2013) ("With expert testimony split, as it often is, the state court chose to credit [two experts] over [a third expert], and we cannot say from this vantage that it was unreasonable to do so"); cf. Franklin , 695 F.3d at 449 , Carter must show that the Supreme Court of Ohio was unreasonable to credit the opinions of Drs. Palumbo and Alcorn.

He does not come close to doing so. In his brief, Carter points to evidence that he claims was "enough" to establish his incompetence, such as his family history of schizophrenia, his hallucinations, his attempts at suicide, his desire to plead guilty, and his expressed desire to kill one of his trial counsel. Petitioner Br. 22-26. However, while Carter may very well be correct that such evidence is "enough," the question before us is whether such evidence compels a determination of incompetence, see Collins , 546 U.S. at 341 , 126 S.Ct. 969 . And because not every suicidal person-or everyone who has a family history of schizophrenia, a desire to plead *772 guilty, or a very low opinion of lawyers-is incompetent to stand trial, it does not. Carter therefore fails to carry his burden under 28 U.S.C. § 2254 (d)(2).

ii

As for Carter's assertion that the trial court should have held a third competency hearing sua sponte , the judgment of the Supreme Court of Ohio was not "so lacking in justification that there was an error well understood and comprehended in existing law beyond any possibility for fairminded disagreement." Hill , 881 F.3d at 510 (quoting Richter , 562 U.S. at 103 , 131 S.Ct. 770 ). While Carter's courtroom behavior was outlandish, it was either cumulative of evidence presented at the competency hearings or demonstrated an ability to engage in means-end reasoning to achieve a stated goal. For instance, during the second competency hearing, both Palumbo and Alcorn testified that Carter had expressed a desire to avoid trial and to plead guilty. Specifically, Palumbo informed the trial court that Carter had "state[d that] he want[ed] to plead guilty, he doesn't want to have to go through all of this," while Alcorn said:

[Carter] clearly indicated a wish to be able to plead guilty and get it over with. He said he didn't want to go through a trial .... And [when] I inquired whether he would prefer to plead guilty and not have to go through a trial so that he wouldn't have to sit through a recitation of the terrible things that he had done[,] ... he agreed with me about that.

Given this, Carter's standing up in open court and declaring his desire to plead guilty-while certainly unwise-merely reiterated information that had been considered by the court in its prior competency determinations.

The same is true of Carter's "lunging" at the trial judge. Immediately preceding the incident, Carter repeatedly stated, in chambers, that he did not wish to attend the trial and asked why he would not be allowed to plead guilty. Upon being advised by the court to speak with his lawyer about pleading guilty, Carter said, "I don't want to be here, don't want to be over in the court. Like, if I act up in here or something, like get restrained, they take me over there if I did that?" Carter , 2015 WL 5752139 , at *23. Shortly after the trial judge warned him that there would be repercussions to "acting up" and directed that Carter be taken back to the courtroom, the Petitioner attempted to attack the judge. Ibid. Then, after being restrained, Carter "promised to the Court that he intends to continue that type of activity throughout the trial if he's required to be here." Ibid. On this record, there is no indication that Carter's behavior was anything other than a calculated effort "to be removed from the courtroom[,]" Carter , 734 N.E.2d at 356 n.3, and, thus, that the incident was of the same kind as evidence already considered during the second competency hearing. Accordingly, we cannot say that the Supreme Court of Ohio unreasonably applied clearly established federal law when it adjudicated this subclaim.

IV

A

Carter's remaining causes of action involve allegations of ineffective assistance of trial counsel. Specifically, Carter argues that his counsel were constitutionally ineffective because they neither (1) protected his right to be competent to stand trial nor (2) properly presented mitigating evidence during the trial's penalty phase. Petitioner Br. 33, 47. Because these claims are analyzed under the same framework, we group them together for ease of exposition.

*773 To succeed on an ineffective-assistance-of-trial-counsel claim, a defendant must make two showings. First, he must show that counsel's performance was deficient, i.e., that "counsel made errors so serious that counsel was not functioning as the 'counsel' guaranteed the defendant by the Sixth Amendment." Strickland v. Washington , 466 U.S. 668 , 687, 104 S.Ct. 2052 , 80 L.Ed.2d 674 (1984). This requires the defendant to identify specific acts or omissions by the counsel that were "outside the wide range of professionally competent assistance." Id. at 690 , 104 S.Ct. 2052 . When reviewing counsel's performance, we "indulge a strong presumption" that "under the circumstances, the challenged action 'might be considered sound trial strategy.' " Id. at 689 , 104 S.Ct. 2052 (quoting Michel v. Louisiana , 350 U.S. 91 , 101, 76 S.Ct. 158 , 100 L.Ed. 83 (1955) ).

Second, the defendant must establish that "the deficient performance prejudiced the defense." Id. at 687, 104 S.Ct. 2052 . For an error to be prejudicial, "[i]t is not enough ... that [it] had some conceivable effect on the outcome of the proceeding." Id. at 693 , 104 S.Ct. 2052 . Rather, there must be "a reasonable probability that, but for counsel's unprofessional errors, the result of the proceeding would have been different." Id. at 694 , 104 S.Ct. 2052 . "A reasonable probability is a probability sufficient to undermine confidence in the outcome." Ibid. Where a defendant challenges a death sentence, the question at this stage is "whether there is a reasonable probability that, absent the errors, the sentencer ... would have concluded that the balance of aggravating and mitigating circumstances did not warrant death." Id. at 695 , 104 S.Ct. 2052 .

Because AEDPA applies to this case, Carter faces a particularly daunting task in establishing ineffective assistance of counsel. Where a state court has adjudicated an ineffective-assistance-of-counsel claim on the merits, we use a "doubly deferential standard of review that gives both the state court and the defense attorney the benefit of the doubt." Titlow , 571 U.S. at 15 , 134 S.Ct. 10 (quotation marks omitted) (emphasis added) (citing Pinholster , 563 U.S. at 190 , 131 S.Ct. 1388 ). In other words, rather than simply examining whether counsel satisfied Strickland 's deferential standard, we ask "whether there is any reasonable argument that counsel satisfied Strickland 's deferential standard." Richter , 562 U.S. at 105 , 131 S.Ct. 770 (emphasis added).

B

Carter's second claim details three ways in which trial counsel were allegedly ineffective in protecting his right to be competent to stand trial: (1) by not presenting "material and relevant information regarding Carter's predisposition to and symptoms of mental illness[,]" (2) by not presenting "additional evidence of Carter's continual decline into incompetency[,]" and (3) by not "request[ing] a competency hearing after the commencement of trial." Petitioner Br. 33. More specifically, Carter faults his counsel for, respectively, (1) "fail[ing] to provide reports by psychiatric social worker Albert Linder and psychologist Dr. Douglas Darnall to any of the experts ... [, which described] Carter [as] suffering from symptoms [indicative of] a major psychiatric disorder" and failing to adequately investigate and present evidence of Carter's suicide attempts; (2) not testifying during the competency hearings "about their personal experience in attempting to work with Carter and the effect of the breakdown in communication on their ability to prepare a constitutionally adequate defense"; and (3) not requesting a third competency hearing following Carter's outbursts at the start of the trial. Id. at 40-44.

*774 Carter presented part of this claim on direct appeal and then again during postconviction proceedings. In both instances, Carter asserted that trial counsel had failed to "fully present evidence of incompetence" because they neither testified about nor filed affidavits detailing their experience of working with Carter. On direct appeal, the Supreme Court of Ohio rejected Carter's argument, stating that it was "speculative" in light of the record. Carter , 734 N.E.2d at 356 . On postconviction appeal, the Court of Appeals of Ohio rejected Carter's claim, finding that Carter's "inability or unwillingness to aid his attorneys in the defense of his case [was] well-documented in the record." Carter , 2000 Ohio App. LEXIS 5935, at *13. Because this claim was adjudicated on the merits in state postconviction proceedings, see Gonzales , 568 U.S. at 75 , 75 n.16, 133 S.Ct. 696 , the question before us is "whether there is any reasonable argument that counsel satisfied Strickland 's deferential standard." Richter , 562 U.S. at 105 , 131 S.Ct. 770 . 9

There is. To see why, it first bears repeating that because Carter's claim was adjudicated on the merits, our review is limited to the record that was before the Ohio Court of Appeals, Pinholster , 563 U.S. at 185 , 131 S.Ct. 1388 (holding, inter alia , that "evidence introduced in federal court has no bearing on § 2254(d)(1) review"). Accordingly, in reviewing Carter's ineffective-assistance-of-trial-counsel claim, we may not consider the reports of Linder and Darnall, which were introduced for the first time during federal habeas proceedings. This makes sense, as when we conduct a § 2254(d)(1) review, we are reviewing the decision of the state court, not the underlying claim.

Moving on to Carter's assertion that counsel were constitutionally ineffective for failing to present evidence of his *775 suicide attempts and for not testifying about the breakdown in their relationship with Carter, the subclaim is meritless because he does not establish prejudice. It is undisputed that witnesses at the two competency hearings testified regarding these matters. At the first hearing, which Palumbo attended, a Trumbull County deputy sheriff informed the court that he had objected to the removal of Carter's handcuffs at the hearing because Carter had attempted to commit suicide while in custody. Then, at the second competency hearing, Dr. King relayed conversations that he had had with Carter's counsel regarding the difficulties they had faced in working with the Petitioner:

I've had conversations with his counsel as frequent as today and they have indicated to me that he is uncooperative with them, he is not working with them, that actually he is very hostile when put under any pressure, and that they are actually not only apprehensive but even afraid of him.

Carter , 2015 WL 5752139 , at *28. King also testified that Carter had expressed a desire to kill one of his trial counsel-whom Carter deemed to be an "idiot," to be "playing slick," and to not caring about the case-and that he (King) believed the threat to be sincere. And in case the court somehow overlooked the depth of Carter's antipathy towards counsel, it was driven home by Alcorn, who testified that Carter had "specifically requested that I inform the court that Mr. Consoldane was a, quote, 'Dumb fuck.' " Based upon this record, there is a reasonable argument to be made that any additional evidence on these matters would have been cumulative and thus would not have generated a reasonable probability that the outcome of the competency hearings would have been different. The district court therefore correctly determined that the Ohio Court of Appeals did not unreasonably apply Strickland when adjudicating this subclaim. Carter , 2015 WL 5752139 , at *26.

Finally, because there is no merit to Carter's claim that the trial court erred in failing to hold a third competency hearing sua sponte , see supra pp. 771-72, there is also no merit to his subclaim that counsel were constitutionally ineffective for failing to request a competency hearing after the commencement of trial, see Franklin , 695 F.3d at 451 ("[T]here being no merit to the underlying claim (trial-court error in not sua sponte ordering another hearing), there could be no merit to th[e] claim [that trial counsel were ineffective in the guilt phase in failing to request another competency hearing.]"). After all, to establish ineffective assistance of counsel, Carter must show that there is a reasonable probability that save for counsels' errors, the result of the proceedings would have been different. Strickland , 466 U.S. at 694 , 104 S.Ct. 2052 . The problem for Carter is that the trial court was aware of almost all of the evidence that he now cites in support of this ineffective-assistance-of-counsel subclaim. See Petitioner Br. 45. For instance, during the two competency hearings, the court had been made aware of Carter's suicide attempts and of the difficult relationship that existed between Carter and his attorneys. And the trial judge had witnessed first-hand Carter's courtroom antics, including his attempt to attack the judge. Given this-and given that we cannot consider Carter's remaining evidence, namely, the reports of Linder and Dr. Darnall-a reasonable argument can be made that trial counsels' failure to request a third competency hearing did not prejudice Carter.

C

In his third, and final, cause of action, Carter contends that counsel failed in two ways to "adequately investigate, prepare, and present mitigating evidence that was *776 available at the time of [his] trial." Petitioner Br. 47. First, Carter argues that counsel did a poor job explaining the evidence introduced during the trial's penalty phase and did not accurately portray Carter's character, history, and background. Ibid. Most notably, Carter criticizes counsel for their decision to decline the trial court's offer of an MRI for mitigation purposes-which, Carter contends, would have shown that he was suffering from organic brain damage. Id. at 54-55. As evidence of his trial counsels' ineffectiveness, he also points to the numerous documents that were submitted to the district court when he litigated his competence to assist habeas counsel. Id. at 59-60.

Second, Carter criticizes counsels' mitigation theory-namely, that Carter suffers from Antisocial Personality Disorder-as "incoherent and damaging." Id. at 50. Instead of presenting the jury with "an image of a mechanical killer who was unable to feel emotion, have sympathy for others or express remorse[,]" Carter contends that counsel should have introduced "information about the impact a structured prison environment could have [had] on Carter[.]" Id. at 47. Lastly, the Petitioner argues that relief is warranted because counsel presented a "mercy theory" of mitigation, which was not permitted in Ohio at the time of his trial. Id. at 53-54.

Carter's claim evolved at various stages of the proceedings. On direct appeal, Carter limited himself to arguing that counsel were ineffective for failing to accept the trial court's offer of MRI testing. The Supreme Court of Ohio concluded that the claim was not appropriately considered on direct appeal as there was "no way of knowing what, if anything, would have been discovered[.]" Carter , 734 N.E.2d at 357 . During postconviction proceedings, however, Carter expanded his focus, asserting that counsel were ineffective for failing to fully investigate his medical and social history-which, presumably, includes their failure to pursue neurological testing-and for failing to hire a mitigation expert to assist in the discovery of relevant information. Carter , 2000 Ohio App. LEXIS 5935, at *8. After detailing the testimony of two mitigation experts who testified at Carter's sentencing hearing, the Court of Appeals of Ohio rejected these assertions as "not [being] supported by the record." Id. at *9-10.

i

Concerning Carter's first subclaim-that trial counsel did not adequately investigate or present mitigating evidence-the judgment of the Ohio Court of Appeals did not involve an unreasonable application of clearly established federal law. Because Carter's claim was adjudicated on the merits in state court, see id. at *10; see also Gonzales , 568 U.S. at 75 , 75 n.16, 133 S.Ct. 696 , our review is limited to the record that was before the Ohio Court of Appeals, Pinholster , 563 U.S. at 185 , 131 S.Ct. 1388 . The district court was therefore correct not to consider "evidence developed in federal habeas proceedings[,]" to wit, the Magee affidavit, the Linder report, the Darnall letter, the 1994 Portage County Juvenile Court chemical-dependency assessment, and an affidavit stating that Carter had been enrolled in a learning-disability program while in elementary school. See Petitioner Br. 59-60; see also 2015 WL 5752139 , at *33, 36, 38.

Absent the foregoing evidence, there is simply no basis for concluding that counsel "failed to fairly depict Carter's character, history and background, including his childhood neglect and trauma, serious mental illness, family history of mental illness, [and] substance abuse[,]" Petitioner Br. 47. As the Court of Appeals of Ohio observed, two defense witnesses testified extensively on these matters during the trial's mitigation phase. See *777 Carter , 2000 Ohio App. LEXIS 5935, at *9-10. For instance, Nancy Dorian, a psychologist who oversaw Carter's foster placement on behalf of children's services, recounted the emotional difficulties he experienced at a young age-such as having an attachment disorder, being "schizoid-prone," and having difficulty getting along with others-as well as the abuse that he suffered at the hands of his mother, e.g., his being "tied to a chair and left alone" for long periods of time. See id. at *9. Likewise, Dr. Sandra McPherson, a clinical psychologist who conducted a thorough review of Carter's medical and social history, detailed the Petitioner's traumatic first few years of life; how he later suffered from emotionally-triggered seizures, an attachment disorder, and hearing issues due to neglect; how he was removed from a foster situation that was his "only chance" for a positive outcome and placed with a family that was emotionally abusive; how he was removed from that family and eventually placed with the Carters, who were not prepared to deal with his many psychological issues; and his genetic predisposition to schizophrenia. In light of this testimony-and the over 200 pages of social service, medical, and legal records that were introduced during the mitigation phase of the trial-trial counsels' performance was not "outside the wide range of professionally competent assistance" with respect to the presentation of evidence of Carter's childhood trauma, mental illness, and substance abuse. See Strickland , 466 U.S. at 690 , 104 S.Ct. 2052 .

Carter's first subclaim therefore rests upon his counsels' seemingly curious decision not to obtain neurological testing for Carter; upon closer examination, however, that decision did not amount to deficient performance in light of Dr. King's testimony at the second competency hearing. In reviewing counsels' decision, it is important to keep in mind that "[a] licensed practitioner is generally held to be competent, unless counsel has good reason to believe to the contrary." Fautenberry v. Mitchell , 515 F.3d 614 , 625 (6th Cir. 2008) (alteration in original) (quoting Lundgren v. Mitchell , 440 F.3d 754 , 772 (6th Cir. 2006) ). Given this, unless a petitioner shows that counsel had "good reason" to believe the practitioner to be incompetent, "it [is] objectively reasonable for counsel to rely upon the doctor's opinions and conclusions." Ibid. Here, when King was asked by the trial judge at the second competency hearing whether "an MRI would ... assist us in this case to render any psychological opinions involving either sanity or competency or mental defect [,]" King replied "no." 10 Given that Carter does not suggest that King was incompetent, and given that counsels' mitigation strategy centered on Carter's traumatic upbringing and subsequent mental illness, counsel could have plausibly determined that an MRI would not have furthered Carter's defense. 11 It therefore cannot be said that *778 Carter's counsels' performance was constitutionally deficient, let alone that there is no reasonable argument that counsel satisfied Strickland 's deferential standard, Richter , 562 U.S. at 105 , 131 S.Ct. 770 .

ii

The second half of Carter's third cause of action-that counsel were constitutionally ineffective because their mitigation theory was objectively unreasonable, see Petitioner Br. 52-is likewise meritless. To begin with, contrary to Carter's suggestions, Ohio state law recognizes Antisocial Personality Disorder ("ASPD") as a statutory mitigating factor. See Esparza v. Sheldon , 765 F.3d 615 , 623 (6th Cir. 2014) (citing State v. Seiber , 56 Ohio St.3d 4 , 564 N.E.2d 408 , 416 (1990) ). Specifically, in Ohio, ASPD qualifies as a mitigating factor pursuant to O.R.C. § 2929.04(B)(7), Seiber , 564 N.E.2d at 416 ; see also State v. Wesson , 137 Ohio St.3d 309 , 999 N.E.2d 557 , 583 (2013) (considering personality disorder with antisocial features as a mitigating factor), a catchall provision that permits a jury to consider "[a]ny other factors that are relevant to the issue of whether the offender should be sentenced to death[,]" O.R.C. § 2929.04(B)(7). Moreover, given that we have recognized that "the failure to introduce evidence of a similar disorder" can be prejudicial, even under AEDPA's deferential standard, Esparza , 765 F.3d at 623 (citing Williams v. Anderson , 460 F.3d 789 , 805 (6th Cir. 2006) ), there is no basis for Carter's suggestion that it was per se ineffective performance for counsel to present evidence of Carter's ASPD, see Petitioner Br. 51 ("It is well accepted, since at least 1988 ... that the defense presentation of [ASPD] ... is not mitigating evidence that favors a life sentence.").

Nor was the choice of mitigation strategy otherwise deficient. As noted earlier, to succeed on an ineffective-assistance-of-counsel claim, a petitioner must overcome the presumption that the challenged action constituted sound trial strategy. Strickland , 466 U.S. at 689 , 104 S.Ct. 2052 . While it is true that counsels' mitigation theory did not present Carter in a flattering light, it was clear and coherent given the available evidence, for instance, the fact that Drs. Palumbo, King, Alcorn, and McPherson had all diagnosed Carter with ASPD. Simply put, counsel sought to lessen Carter's blameworthiness for a brutal crime by leveraging an uncontested psychiatric diagnosis to explain "how [Carter] developed and why he developed the way he did[.]" Counsels' strategy, then, was to impress upon the jury the importance of judging Carter by a different standard when assessing the wrongfulness of his actions than it would judge one who, despite having been nurtured as a child, had chosen to commit the crime in question. It cannot plausibly be said that counsels' reliance on nuanced moral reasoning-i.e., that an individual's blameworthiness for a given act can change based upon the circumstances of his or her upbringing-fell outside the wide range of professionally competent assistance.

To be clear, counsels' strategy was not a plea for mercy. Carter is quite correct that had defense counsel simply *779 made a plea for mercy, their performance would have been, at minimum, deficient. That is because in Ohio, mercy "is not a mitigating factor and thus [is] irrelevant to sentencing[.]" State v. Lorraine , 66 Ohio St.3d 414 , 613 N.E.2d 212 , 216 (1993). However, notwithstanding the district court's characterization of counsels' theory of mitigation as a "plea for mercy," Carter , 2015 WL 5752139 , at *35, defense counsel never argued as such. Rather, as detailed above, their argument was premised on a statutorily recognized mitigating factor. Given that Carter's entire argument here rests upon the district court's mischaracterization, there is no merit to it.

Finally, while Carter may be correct that an alternative mitigation theory would have been more successful, that does not show that the Ohio courts unreasonably applied clearly established federal law in rejecting his Strickland claim. The sole basis for Carter's alternative mitigation theory is an affidavit by Dr. Bob Stinson-a psychologist who examined the records available to the trial attorneys at the time of the mitigation hearing-that was introduced during federal habeas proceedings. As we have repeatedly noted, however, we cannot consider such evidence when reviewing a claim adjudicated on the merits in state court. Pinholster , 563 U.S. at 185 , 131 S.Ct. 1388 . Accordingly, other than his bald assertion that evidence of adaptability to life in prison is "a vital component of any mitigation presentation where the jury is choosing between life and death[,]" Petitioner Br. 60-61 (emphasis added), Carter provides no grounds for discarding the strong presumption that counsels' decision constituted sound trial strategy, see Strickland , 466 U.S. at 689 , 104 S.Ct. 2052 , let alone that he was prejudiced by their decision. Thus, counsel were not constitutionally ineffective for their choice of mitigation strategy.

V

For the foregoing reasons, we AFFIRM the decision of the district court denying the petition for a writ of habeas corpus.