Heath Alan Thompson (“Thompson”), Texas prisoner # 1308793, was convicted by a jury of burglary of a habitation with intent to commit sexual assault and was sentenced to forty years of imprisonment. The district court denied his application for habeas relief under 28 U.S.C. § 2254. This court granted a certificate of appealability (“COA”) to determine “whether [Thompson’s] counsel was ineffective in failing to object at the punishment phase to the victim-impact testimony of Wray Foster.” Foster testified about injuries she received in a separate incident as a passenger in Thompson’s car which was in an accident while Thompson was driving under the influence. We now AFFIRM the district court’s denial of habeas relief.
I. Background
A jury convicted Thompson of one count of burglary of a habitation with intent to commit sexual assault. At the punishment phase, the State presented evidence that Thompson had two prior convictions for driving while intoxicated (DWI). The State also presented the testimony of Wray Foster, Thompson’s passenger during his second DWI, who was paralyzed when Thompson had an accident on that occasion. Foster came into the courtroom in a wheelchair and testified that as a result of the accident, she was hospitalized for two months, had extensive scars, and was confined to a wheelchair because of a broken back. Thompson’s counsel never objected to this testimony. The jury ultimately sentenced Thompson to forty years’ imprisonment. Thompson’s conviction and sentence were affirmed on appeal.
*378On November 13, 2006, Thompson filed a motion with the state court for post-conviction relief, alleging numerous defects at trial. During an eight-day evidentiary hearing, Thompson’s counsel testified that he acted pursuant to an objection-minimization strategy, but he did not realize he could have objected to Foster’s testimony as extraneous victim-impact evidence. The court ultimately denied Thompson’s request for post-conviction relief. As part of its denial, the state court concluded that Thompson’s counsel’s strategy of objection-minimization was reasonable. The court further found that Thompson’s counsel was not ineffective for failing to object to Foster’s testimony because the testimony was relevant to sentencing and admissible. The Texas Court of Criminal Appeals (“TCCA”) adopted the findings of the trial court and denied Thompson’s appeal without written order.
Thompson then filed the instant § 2254 petition, in which he continued to allege, among other claims, that his counsel was ineffective for failing to object to Foster’s testimony. The district court denied Thompson’s petition, noting that it was bound by the state courts’ determination that state evidentiary law was not violated, and that Thompson had failed to identify how the testimony violated any of his federal rights. Thompson requested a COA, which this court granted only as to whether Thompson’s counsel was ineffective in failing to object to Foster’s “victim-impact” testimony.
II. Analysis
On an appeal of a denial of habeas relief, we review the district court’s findings of fact for clear error and its legal conclusions de novo. Martinez v. Johnson, 255 F.3d 229, 237 (5th Cir.2001). Thompson argues that the district court erred in finding that his attorney’s failure to object to Foster’s testimony did not amount to ineffective assistance of counsel. To succeed on a claim of ineffective assistance of counsel, Thompson must demonstrate: (1) that his counsel’s performance was deficient, and (2) that the deficient performance prejudiced his defense. See Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984); Schaetzle v. Cockrell, 343 F.3d 440, 444 (5th Cir.2003). Moreover, because Thompson was convicted in state court, Thompson must demonstrate that the state courts’ conclusion that he had not proven a Strickland claim was unreasonable in light of Supreme Court precedent. 28 U.S.C. § 2254(d); see also Thaler v. Haynes, — U.S. -, -, 130 S.Ct. 1171, 1173, 175 L.Ed.2d 1003 (2010) (“A legal principle is clearly established within the meaning of [28 U.S.C. § 2254(d)(1) ] only when it is embodied in a holding of this Court.”); Woodfox v. Cain, 609 F.3d 774, 800 & n. 14 (5th Cir.2010).
The only issue before this court is whether the failure of Thompson’s counsel to object to the admission of Foster’s testimony denied Thompson of his constitutional right to counsel. See Yarborough v. Gentry, 540 U.S. 1, 8, 124 S.Ct. 1, 157 L.Ed.2d 1 (2003) (“The Sixth Amendment guarantees reasonable competence, not perfect advocacy judged with the benefit of hindsight.”). Thompson’s sole argument before the state habeas court was that his attorney was constitutionally deficient for failing to object to Foster’s testimony on the grounds that it was irrelevant under Texas Rule of Evidence 401 as interpreted by the TCCA in Cantu v. State, 939 S.W.2d 627, 637 (Tex.Crim.App.1997).1 *379The state habeas court held that Foster’s testimony in this case was relevant to sentencing under Texas Code of Criminal Procedure art. 37.07 § 3, and that the testimony was therefore admissible. This finding was upheld by the TCCA. This court must defer to the state courts’ ruling that Foster’s testimony was admissible under the state’s evidentiary law. See Charles v. Thaler, 629 F.3d 494, 500-01 (5th Cir.2011) (“A federal court lacks authority to rule that a state court incorrectly interpreted its own law. When, as here, a state court’s legal conclusions are affirmed by the highest court in that state, those conclusions are state law.”); Schaetzle, 343 F.3d 440, 449 (5th Cir.2003) (“ ‘It is not our function as a federal appellate court in a habeas proceeding to review a state’s interpretation of its own law.’ ” (quoting Weeks v. Scott, 55 F.3d 1059, 1063 (5th Cir.1995))).2
Because the state courts held that Foster’s testimony was admissible, Thompson’s counsel’s failure to object to it on the grounds that it was inadmissible under state law could not be deficient performance. See Charles, 629 F.3d at 501 (“The testimony was admissible; counsel did not err.”). Thus, Jones v. Cain, 600 F.3d 527, 536 (5th Cir.2010), upon which Thompson relies, is inapposite. In Jones, the Confrontation Clause claim that the court addressed was independent of the state courts’ hearsay ruling. See id. In this case, Thompson’s ineffective assistance of counsel argument is precluded by the state courts’ findings that the evidence was admissible and any objection on those grounds would have been futile.
Furthermore, although some evidence can be so unduly prejudicial that its admission constitutes a violation of federal due process rights, see Payne v. Tennessee, 501 U.S. 808, 825, 111 S.Ct. 2597, 115 L.Ed.2d 720 (1991), Thompson has exhausted neither a Fourteenth Amendment claim to the admission of the evidence nor a Sixth Amendment claim for his lawyer’s failure to object to the evidence on federal due process grounds.3 In any event, he *380does not point to a Supreme Court case that makes this testimony inadmissible as a matter of federal constitutional law.
We have no jurisdiction over Thompson’s other arguments, which are beyond the scope of the COA.
III. Conclusion
For the foregoing reasons, the district court’s denial of habeas relief is AFFIRMED.