Shannon Thomas seeks a certificate of appealability (“COA”) from the denial of his petition for a writ of habeas corpus pursuant to 28 U.S.C. § 2254. Because Thomas cannot make a substantial showing of the denial of a federal constitutional right, we deny a COA.

I.

On Christmas Eve 1993, Thomas and his friend Keith Clay entered the home of *528 Roberto Rios, a marihuana dealer. Thomas and Clay robbed Rios, then murdered him by shooting him three times and stabbing him in the neck with a pair of scissors. Thomas then went upstairs and executed Rios’s two children, ten year-old Maria and eleven year-old Victor, by shooting each in the head through a pillow as they lay side-by-side on the floor.

The murders remained unsolved for over a year, until the police received information from Joseph “Boo” Jones, a friend of Clay and Thomas. After his arrest, Thomas gave the police two written statements. In the first, he acknowledged purchasing narcotics from Rios that day but denied any knowledge of the killings. In his second statement, Thomas asserted that Clay had acted alone in killing the Rios family after Thomas had left the residence.

Thomas was indicted for the capital murder of Victor Rios. At trial, no physical evidence was presented to link him to the murders. He was inculpated, however, by an abundance of circumstantial evidence, including information that he possessed a gun similar to the murder weapon. In addition, the state presented testimony linking him to the robbery and murders. Three witnesses testified that Thomas had asked them to participate in robbing Rios; two of them stated that Thomas had admitted the murders to them. One of the witnesses, Jones, agreed to tape record a conversation with Thomas at the request of the police, in which Thomas made incriminating statements about the murders.

Additionally, evidence put Thomas at the scene of the crime, including the statement of a postal worker, Earl Guidry, who saw two men leaving the Rios home near the time of the killings. Guidry tentatively identified Thomas after undergoing hypnosis and participating in several photograph identification arrays and one live line-up. Another witness testified that he saw a car resembling Clay’s near the Rios residence shortly before the murders.

Thomas was convicted, and the jury answered the special issues in a manner requiring the imposition of a death sentence. The Texas Court of Criminal Appeals affirmed the conviction and sentence on direct appeal. Thomas v. State, No. 72,701 (Tex Crim.App. Mar. 31, 1999). Thomas did not seek a writ of certiorari.

While his direct appeal was pending, Thomas sought state habeas relief, which was denied by the Court of Criminal Appeals. Ex Parte Thomas, No. 51,306-01 (Tex.Crim.App. Mar. 20, 2002). Thomas then filed for a federal writ of habeas corpus under § 2254, raising six claims of error. The district court dismissed the claims on summary judgment and refused to grant a COA. Thomas v. Dretke, No. H-03-CV-988 (S.D.Tex. Dec. 10, 2003). Thomas now seeks a COA on two of his claims.

II.

Our review on a request for a COA is highly circumscribed by statute. Pursuant to the Anti-Terrorism and Effective Death Penalty Act of 1996 (“AEDPA”), to be entitled to relief a petitioner must show that the state court resolution of his case was either “contrary to, or involved an unreasonable application of, clearly established federal law, as determined by the Supreme Court of the United States” or “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.” 28 U.S.C. § 2254(d). 1 This high level of deference to *529 state court proceedings “embodies the principles of federalism, comity, and finality of judgments.... ” Evans v. Cockrell, 285 F.3d 370, 374 (5th Cir. 2002).

To grant a COA, however, we need not decide the ultimate merits of the underlying habeas petition; we ask only whether the petitioner has made “a substantial showing of the denial of a constitutional right.” 28 U.S.C. 2253(c)(2). “A petitioner satisfies this standard by demonstrating that jurists of reason could disagree with the district court’s resolution of his constitutional claim or that jurists could conclude the issues presented are adequate to deserve encouragement to proceed further.” Miller-El v. Cockrell, 537 U.S. 322, 327, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003). That is, our duty is to determine not whether Thomas is entitled to relief, but whether the district court’s conclusion (that the state court adjudication was not contrary to or an unreasonable application of federal law) is one about which jurists of reason could disagree. Furthermore, other doctrines bridle habeas relief, including the harmless error doctrine. See Brecht v. Abrahamson, 507 U.S. 619, 637, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993).

III.

Thomas petitions for a COA based on an argument that his constitutional rights were violated by the admission of Guidry’s in-court identification; he asserts that it was impermissibly tainted by suggestive pre-trial identification procedures under Simmons v. United States, 390 U.S. 377, 88 S.Ct. 967, 19 L.Ed.2d 1247 (1968). Although he expends much breath in analyzing the two-prong test established under Simmons v. United States and its progeny, we focus on the analysis performed by the Court of Criminal Appeals and the district court. Both courts concluded that even assuming arguendo that the admission of the testimony was unconstitutional, the error was harmless in light of the overwhelming evidence corroborating the content of the witnesses’ testimony.

A habeas petitioner has the burden of demonstrating “actual prejudice” from the alleged constitutional error. Brecht, 507 U.S. at 637. Under Brecht, the appropriate harmless error standard on collateral review is the test established by Kotteakos v. United States, 328 U.S. 750, 66 S.Ct. 1239, 90 L.Ed. 1557 (1946), under which there has to be more than a reasonable possibility that it contributed to the verdict; the error must have had a “substantial effect or influence in determining the verdict.” Woods v. Johnson, 75 F.3d 1017, 1026 (5th Cir. 1996) (emphasis added). The district court meticulously laid out how the other evidence presented by the state corroborated and was cumulative of both of the elements that Guidry’s in-court identification and testimony supported: (1) that Thomas was at or near the Rios residence at the established time of the murders; and (2) the impeachment of Thomas’s statement that claimed that he left the residence by himself before Clay did, implying that Clay acted alone in murdering the family.

First, although Guidry’s identification placed Thomas at the crime scene, it was far from the only evidence that did so. Beyond other circumstantial corroborating evidence, this element of the state’s case was most plainly demonstrated by Thomas’s own admission — in his voluntary statement to the police — that he was present. Given the great mass of particularly credible evidence supporting this fact, we cannot conclude that reasonable jurists *530 could disagree as to the district court’s finding that admitting the testimony was harmless for establishing this element.

Further, Guidry’s testimony, claiming that he observed Clay and Thomas leaving the Rios residence together, refuted Thomas’s claim that he “left home alone and waited in the car after he bought some marijuana ... [until] Clay came out of the home fifteen minutes later with blood on his pants.” Thomas v. State, No. 72,701, at 9 (Tex.Crim.App. Mar. 31, 1999). As the district court articulated, the testimony of numerous witnesses also undercut Thomas’s statement to the police and his claim that Clay acted alone in killing the family while Thomas waited in the vehicle. No less than three of Thomas’s own friends competently testified that Thomas had confessed the killings to them.

Thomas attempts to meet his burden of establishing that admitting the testimony subjected him to actual prejudice, because all that remained was unreliable “biased” testimony, because it came from witnesses paid to testify by the police or subject to cooperation deals to obtain assistance in their own cases. This argument is unavailing; the bias of the remaining witnesses was appropriately the subject of cross-examination and is customary grist for the jury mill. We deny a COA regarding the admission of Guidry’s identification testimony, because given the extensive mass of evidence that was present, reasonable jurists could not disagree as to the district court’s sound finding that the Court of Criminal Appeals was reasonable in its conclusion that it was harmless under Brecht. 2

IV.

Thomas applies for a COA on the issue of whether the state court violated his right to due process under the Fourteenth Amendment by failing to instruct the jury that, if given a life sentence, he would be eligible for parole in forty years. At trial, the court forbade any reference to the potential for parole eligibility that is available for prisoners serving life sentences for capital murder in Texas. Although Texas subsequently has allowed for jury instructions regarding parole eligibility in capital murder cases, 3 this was not the case at the time of Thomas’s trial. The jury was forced to consider the issue of his future dangerousness without hearing testimony or argument regarding the possibility of his release on parole if given a life sentence.

Thomas contends it was error to keep the information about his parole eligibility from the jury based on Simmons v. South Carolina, 512 U.S. 154, 169, 114 S.Ct. 2187, 129 L.Ed.2d 133 (1994), where the Court concluded that the possibility of a life sentence without possibility of parole is relevant to a jury’s determination of whether the defendant poses future harm to society. To support his position, Thomas points to language in Simmons v. South *531 Carolina saying that “[i]n assessing future dangerousness, the actual duration of the defendant’s prison sentence is indisputably relevant.” Id. at 163.

The Court, however, also specifically delineated that the holding was inapplicable in circumstances in states where parole was available for capital offenses, as is the case in Texas. 4 The Court confirmed the limited nature of the Simmons v. South Carolina holding in Ramdass v. Angelone, 530 U.S. 156, 168, 120 S.Ct. 2113, 147 L.Ed.2d 125 (2000), stating that “Simmons applies only to instances where, as a legal matter, there is no possibility of parole if the jury decides the appropriate sentence is life in prison.” Moreover, as the district court observed, we have repeatedly rejected similar claims seeking to extend Simmons v. South Carolina to the Texas capital sentencing procedure. 5

Because there is no well-settled federal law supporting Thomas’s position, AEDPA precludes federal courts from granting relief, because it cannot be said that the state court’s application of federal law was objectively unreasonable. Because binding precedent forecloses relief on this claim, jurists of reason could not disagree with the district court’s decision to dismiss this claim, and therefore the request for a COA is DENIED. 6