Robert William Tear, Texas prisoner # 1024018, filed a 28 U.S.C. § 2254 petition to set aside his conviction on two counts of aggravated sexual assault of a child under 14 years of age. After the district court dismissed his petition, we issued Tear a certificate of appealability (COA) on the following issues: whether counsel was ineffective for failing to call an expert to testify about the child eomplain-ant’s expressive disorder and whether counsel was ineffective for failing to object to expert testimony regarding the credibility of the complainant in particular and of child sex abuse complainants in general. We now affirm.

If counsel renders a deficient performance that prejudices his client’s defense, he violates his client’s rights under the Sixth Amendment. Strickland v. Washington, 466 U.S. 668, 686, 691-92, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). A deficient performance is one that falls “below an objective standard of reasonableness.” Porter v. McCollum, — U.S.-, 130 S.Ct. 447, 452, 175 L.Ed.2d 398 (2009) (internal quotation marks and citation omitted). A petitioner makes the required showing of prejudice if he demonstrates “that there is a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different.” Id. (internal quotation marks and citation omitted). The probability “of a different result must be substantial, not just conceivable.” Harrington v. Richter, — U.S. -, 131 S.Ct. 770, 792, 178 L.Ed.2d 624 (2011); see also Lamb v. Johnson, 179 F.3d 352, 360 (5th Cir. 1999).

A § 2254 petitioner asserting an ineffectiveness claim must demonstrate that “the state court’s rejection of [the] claim ... was ‘contrary to, or involved an unreasonable application of Strickland, or [that] it rested’ ‘on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.’” Porter, 130 S.Ct. at 452 (quoting § 2254(d)). An ineffectiveness claim presents a mixed question of law and fact. Richards v. Quarterman, 566 F.3d 553, 561 (5th Cir. 2009). In a habeas appeal, “[t]his court reviews the district court’s legal conclusions de novo, applying the *112 same standard as the district court.” Amos v. Scott, 61 F.3d 333, 337-38 (5th Cir. 1995). When examining mixed questions of law and fact, this court uses a de novo standard by independently applying the law to the facts found by the district court, as long as the district court’s factual determinations are not clearly erroneous. Richards, 566 F.3d at 561. A state court’s discreet factual findings are presumed to be correct, but a petitioner may rebut the presumption with clear and convincing evidence. § 2254(d)(2), (e)(1).

Under § 2254, a state habeas court’s merits adjudication is entitled to deference by federal courts. Yarborough v. Alvarado, 541 U.S. 652, 665-66, 124 S.Ct. 2140, 158 L.Ed.2d 938 (2004). To get federal relief, Tear must demonstrate that the Texas court’s denial of habeas relief “was so lacking in justification that there was an error well understood and comprehended in existing law beyond any possibility for fairminded disagreement.” Richter, 131 S.Ct. at 786-87.

After the COA issued in the instant case, the Supreme Court held that a federal court adjudicating a claim under § 2254(d) is limited to the record that was before the state courts. See Cullen v. Pinholster, — U.S.-, 131 S.Ct. 1388, 1398, 179 L.Ed.2d 557 (2011). Accordingly, review of the district court’s ruling may not rely on the additional factual findings resulting from that court’s evidentiary hearing. See id. Included among those was the finding that, contrary to what the state habeas court found based on the evidence before it, Tear had indeed made this counsel aware of an expressive disorder expert and of her willingness to testify. With that finding now eliminated from consideration, Tear is left with nothing that could constitute the clear and convincing evidence needed to rebut the trial court’s factual findings that he did not inform his trial counsel about the expressive disorder expert and that trial counsel’s affidavit testimony was worthy of belief. See § 2254(e)(1). Therefore, Tear has failed to demonstrate that the Texas court’s denial of this claim was the result of “an unreas-aonable determination of the facts,” § 2254(d)(2), given the evidence before the state court, or “was contrary to, or involved an unreasonable application of’ Strickland. § 2254(d)(1); see also Porter, 130 S.Ct. at 452. Because Tear fails to demonstrate that “there is [no] reasonable argument that counsel satisfied Stride-land’s deferential standard,” this claim fails. Harrington, 131 S.Ct. at 787.

Tear’s second claim fails for two reasons. First, the expert who testified at trial concerning her investigation of the claimant’s assertions of abuse did not offer an opinion concerning the veracity of this complainant in particular, and so there was nothing for counsel to object to in that regard. Second, even if counsel was deficient with regard to expert testimony about the truthfulness of child sexual abuse complainants in general, Tear was not prejudiced because he is unable to show that his conviction probably resulted from the deficiency. Tear has demonstrated that it is conceivable that the jury was persuaded by the expert’s testimony to think that the complainant lied when he uttered an on-the-stand denial of one of the charges against Tear. But such a conceivable possibility of a different result is simply insufficient to demonstrate prejudice. Richter, 131 S.Ct. at 792; Lamb, 179 F.3d at 360. Tear thus failed to establish that “there is [no] reasonable argument that counsel satisfied Strickland’s deferential standard.” Harrington, 131 S.Ct. at 787.

AFFIRMED.