In 1986, a Texas jury convicted and sentenced to death petitioner-appellee Anthony Leroy Pierce for the murder of Fred Eugene Johnson during a robbery of a Church’s Chicken restaurant in 1977. State appellate courts affirmed the conviction and sentence and denied post-conviction relief. Pierce then brought a federal habeas petition under the Antiterrorism and Effective Death Penalty Act (“AED-PA”), 28 U.S.C. § 2254. The district court granted Pierce substantive relief on one of his sentencing claims, concluding that the special issues presented to the jury at the sentencing phase did not properly permit the jury to consider and give effect to Pierce’s mitigating evidence, in violation of Penry v. Lynaugh, 492 U.S. 302, 109 S.Ct. 2934, 106 L.Ed.2d 256 (1989). The district court denied the remaining bases for substantive relief and denied a certificate of appealability (COA) on those issues. The State’s appeal of the district court’s grant of relief under Penry is now before us, as is Pierce’s request for a COA for some of the claims he unsuccessfully raised in the district court. We grant Pierce’s request for a COA as to his claims that he is mentally retarded (rendering him ineligible for the death penalty under Atkins v. Virginia, 536 U.S. 304, 122 S.Ct. 2242, 153 L.Ed.2d 335 (2002)), and that he received ineffective assistance of counsel. Pierce’s request is denied on all other claims.
We reserve opinion on the government’s appeal of the Penry issue until after oral argument, during which we will hear argument as to Pierce’s Penry, Atkins, and ineffective assistance claims.
I. Factual and Procedural Background
The district court’s exhaustive opinion more than adequately documents the factual background and procedural development of this case. See Pierce v. Quarterman, No. H-07-1561, 2008 WL 4445064 (S.D.Tex. Sept.26, 2008). Here, we recite only so many of the facts and procedure as are necessary to provide a framework for our grant in part and denial in part of a COA.
Pierce was indicted for capital murder for the shooting death of Fred Eugene Johnson, the manager of a Church’s Chicken in Houston, during a robbery of that restaurant on August 4, 1977. Pierce’s first two convictions were overturned, in both cases because the trial court had improperly overruled defense counsel’s challenges to certain venire members. See Pierce v. State, 604 S.W.2d 185 (Tex.Crim.App.1980); Pierce v. State, 696 S.W.2d 899 (Tex.Crim.App.1985). Pierce was tried and convicted a third time and sentenced to death in 1986. The Texas Court of Criminal Appeals (TCCA) affirmed the conviction and sentence, Pierce v. State, 777 S.W.2d 399 (Tex.Crim.App.1989), cert. denied, 496 U.S. 912, 110 S.Ct. 2603, 110 L.Ed.2d 283 (1990), and denied his application for postconviction relief, Ex parte Pierce, No. 15859-03 (Tex.Crim.App. Sept. 19, 2001). On August 29, 2002, Pierce filed a successor state habeas application, which the TCCA denied on April 18, 2007. Ex parte Pierce, No. 15859-04, 2007 WL 1139414 (Tex.Crim.App. Apr.18, 2007). Pierce filed a 28 U.S.C. § 2254 federal *787habeas petition on May 9, 2007, an amended federal habeas petition on August 80, 2007, and a supplemental federal habeas petition on July 1, 2008.
Pierce presented thirteen issues to the district court. On cross-motions for summary judgment, the district court granted Pierce relief on the first of these issues: whether the statutory special issues presented to the jury at sentencing, and the prosecutor’s closing arguments regarding those special issues, precluded the jury from “consider[ing] and giv[ing] effect to” Pierce’s mitigating evidence, as Penry v. Lynaugh, 492 U.S. 302, 109 S.Ct. 2934, 106 L.Ed.2d 256 (1989), requires. The district court granted summary judgment to the State on the remaining twelve issues, denying the relief Pierce sought and declining to grant a COA. Pierce now seeks a COA as to five issues on which the district court denied relief.
II. Standards of Review
Pierce’s motion is governed by the applicable provisions of AEDPA. See Lindh v. Murphy, 521 U.S. 320, 335-36, 117 S.Ct. 2059, 138 L.Ed.2d 481 (1997). Under AEDPA, a state habeas petitioner may appeal a district court’s dismissal of his petition only if the district court or the court of appeals first issues a COA. 28 U.S.C. § 2253(c)(1)(B); see also Miller-El v. Cockrell, 537 U.S. 322, 336, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003) (describing a COA as a “jurisdictional prerequisite” without which “federal courts of appeals lack jurisdiction to rule on the merits of appeals from habeas petitioners”). In determining whether to grant a petitioner’s request for a COA, we limit our “examination to a threshold inquiry into the underlying merit of [the petitioner’s] claims.” Miller-El, 537 U.S. at 327, 123 S.Ct. 1029 (citing Slack v. McDaniel, 529 U.S. 473, 481, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000)). “This threshold inquiry does not require full consideration of the factual or legal bases adduced in support of the claims. In fact, the statute forbids it.” Id. at 336,123 S.Ct. 1029.
We will grant a request for a COA “only if the applicant has made a substantial showing of the denial of a constitutional right.” 28 U.S.C. § 2253(c)(2). In order to grant a COA for one of Pierce’s substantive claims, we must conclude only that Pierce has demonstrated the threshold showing for that substantive claim. See Miller-El, 537 U.S. at 327, 123 S.Ct. 1029. “Although the issuance of a COA ‘must not be pro forma or a matter of course,’ the petitioner satisfies the burden under § 2253(c) ‘by demonstrating] that reasonable jurists would find the district court’s assessment of the constitutional claims debatable or wrong.’ ” Pippin v. Dretke, 434 F.3d 782, 787 (5th Cir.2005) (alteration in original) (quoting Miller-El, 537 U.S. at 337-38, 123 S.Ct. 1029). “[A] claim can be debatable even though every jurist of reason might agree, after the COA has been granted and the case has received full consideration, that petitioner will not prevail.” Miller-El, 537 U.S. at 338, 123 S.Ct. 1029. “[A]ny doubt as to whether a COA should issue in a death-penalty case must be resolved in favor of the petitioner.” Pippin, 434 F.3d at 787.
In determining whether the district court’s denial of Pierce’s petition for a COA on his claims was debatable, we must keep in mind the deferential standard of review that AEDPA requires a district court to apply to the state court’s rulings. See Brown v. Dretke, 419 F.3d 365, 371 (5th Cir.2005) (‘With respect to the review of factual findings, AEDPA significantly restricts the scope of federal habeas review.”). Under AEDPA,
a federal court is not to grant a writ of habeas corpus “with respect to any claim that was adjudicated on the merits in State court proceedings” unless it deter*788mines that the state court’s adjudication “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.”
Pippin, 434 F.3d at 787 (quoting 28 U.S.C. § 2254(d)(1)). Moreover, a “‘determination of a factual issue made by a State court shall be presumed to be correct’ unless the petitioner rebuts the presumption ‘by clear and convincing evidence.’ ” Id. at 788 (quoting 28 U.S.C. § 2254(e)(1)). “This presumption of correctness attaches not only to explicit findings of fact, but also to ‘unarticulated findings which are necessary to the state court’s conclusions of mixed law and fact.’ ” Id. (quoting Pondexter v. Dretke, 346 F.3d 142, 148 (5th Cir.2003)).
Under AEDPA, a federal district court may grant an evidentiary hearing only if the prisoner diligently and reasonably attempted, “in light of the information available at the time, to investigate and pursue claims in state court.” Williams v. Taylor, 529 U.S. 420, 435, 120 S.Ct. 1479, 146 L.Ed.2d 435 (2000); see also 28 U.S.C. § 2254(e)(2)(a)(ii) (“[T]he [district] court shall not hold an evidentiary hearing on the claim unless the applicant shows that ... the claim relies on ... a factual predicate that could not have been previously discovered through the exercise of due diligence.”). For state courts to have a full and fair opportunity to adjudicate the habeas applicant’s constitutional claims, “[diligence will require in the usual case that the prisoner, at a minimum, seek an evidentiary hearing in state court in the manner prescribed by state law.” Williams, 529 U.S. at 437, 120 S.Ct. 1479. Even then, mere requests for an evidentiary hearing will not demonstrate reasonable diligence. Burton v. Terrell, 576 F.3d 268, 273 (5th Cir.2009); Dowthitt v. Johnson, 230 F.3d 733, 758 (5th Cir.2000). “In cases where an applicant for federal habeas relief is not barred from obtaining an evidentiary hearing by 28 U.S.C. § 2254(e)(2), the decision to grant such a hearing rests in the discretion of the district court.” Schriro v. Landrigan, 550 U.S. 465, 468, 127 S.Ct. 1933, 167 L.Ed.2d 836 (2007). A district court’s decision to grant or deny an evidentiary hearing is reviewed for abuse of discretion. Clark v. Johnson, 202 F.3d 760, 765-66 (5th Cir.2000).
III. Analysis
Pierce seeks a COA as to five issues: (1) whether the prosecution’s failure to disclose certain exculpatory evidence violated Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), and therefore entitles Pierce to a new trial; (2) whether the trial court erred in not allowing an architect to testify as an expert witness regarding alleged flaws in the lineup in which Pierce was identified; (3) whether the jury improperly considered extraneous information or otherwise committed misconduct; (4) whether Pierce is a mentally retarded offender whose execution is barred by Atkins v. Virginia, 536 U.S. 304, 122 S.Ct. 2242, 153 L.Ed.2d 335 (2002); and (5) whether Pierce’s trial counsel provided ineffective assistance by failing to investigate and present certain mitigating evidence during the sentencing phase. As to the last three issues, Pierce also contends that the district court abused its discretion in refusing to grant his request for an evidentiary hearing.
A. The Brady Claim
Pierce contends that the district court’s refusal to grant him a new trial under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), was debatable or wrong. Before ruling on the cross-motions for summary judgment on Pierce’s federal habeas petition, the district court granted limited discoveiy as to whether the prosecution had failed to disclose that certain witnesses at Pierce’s *789third trial had received a monetary reward. Documents produced from Pierce’s prosecution file revealed that two of the witnesses who testified against Pierce at all three of his trials, the brothers Reginald and George Sanders (who were aged twelve and fifteen, respectively, at the time of the crime), as well as another teenage witness who did not testify, shared equally in a $1,000 reward that they received shortly after Pierce’s first conviction. The district court acknowledged that this undisclosed evidence would have been material for impeachment but nevertheless denied Brady relief, concluding that there was not a reasonable probability, in light of the other evidence, that disclosure would have changed the outcome of the trial. Pierce v. Quarterman, No. H-07-1561, 2008 WL 4445064, at *25 (S.D.Tex. Sept.26, 2008).
There are three essential components to a Brady prosecutorial misconduct claim: “ ‘The evidence at issue must be favorable to the accused, either because it is exculpatory, or because it is impeaching; that evidence must have been suppressed by the State, either willfully or inadvertently; and prejudice must have ensued.’ ” Banks v. Dretke, 540 U.S. 668, 691, 124 S.Ct. 1256, 157 L.Ed.2d 1166 (2004) (quoting Strickler v. Greene, 527 U.S. 263, 281-82, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999)). Prejudice is established where there exists a “reasonable probability” that had the evidence been disclosed the result at trial would have been different. Id. at 699, 124 S.Ct. 1256. “A ‘reasonable probability’ of a different result is shown when the [statej’s evidentiary suppression ‘undermines confidence in the outcome of the trial.’” See Kyles v. Whitley, 514 U.S. 419, 434, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995) (quoting United States v. Bagley, 473 U.S. 667, 678, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985)).
The district court concluded that the nondisclosure did not prejudice Pierce because the Sanders brothers identified Pierce as the shooter shortly after the murder, provided testimony consistent with that identification at trial, and did not receive the reward money until after the first trial was complete. The district court also noted that there were two additional eyewitnesses, Brenda Charles and Ronald Cooks, who testified that Pierce was the shooter and who did not receive a reward. The state habeas court specifically found, in response to other issues raised in Pierce’s state habeas application, that Charles and Cooks were credible witnesses who had identified Pierce through a legally-appropriate lineup. The district court accepted the state habeas court’s factual and legal conclusions on those issues as reasonable, and Pierce does not seek a COA as to those issues. The district court’s holding that the nondisclosure did not prejudice Pierce because there was no reasonable likelihood that it would have changed the result is not debatable.1 Ac*790cordingly, Pierce’s application for a COA on this issue is denied.
B. The Expert Evidentiary Claim
Pierce next seeks a COA on the issue of whether the trial court improperly excluded the testimony of an architect, Ken Austin, as an expert witness for Pierce. Because the record contained no photograph of Pierce’s lineup, Austin sought to introduce an illustration of the lineup drawn to scale based on the descriptions of the lineup participants in the Houston Police Department’s lineup sheet. Austin also proposed to testify more generally about how perceptions of size are affected by what surrounds the item viewed, and that this phenomenon can influence identification. Austin proposed additional exhibits to illustrate these concepts.
On direct appeal, the TCCA affirmed the trial court’s exclusion of Austin’s proposed illustration of the lineup because Austin could not establish that it was an accurate representation of the lineup. The court based this conclusion on Austin’s admission that he based his drawing on hearsay police reports and did not know if his drawing was an accurate depiction of the lineup. As to Austin’s proposed testimony and other exhibits, the TCCA held that Austin offered no specialized knowledge that was not already possessed by the jurors. See Pierce v. State, 777 S.W.2d 399, 413-14 (Tex.Crim.App.1989). The TCCA reached the same legal conclusions in denying Pierce’s habeas application. The federal district court held that the TCCA had reasonably concluded that Austin’s proposed illustration of the lineup was not competent evidence and that his proposed expert testimony offered the jury no helpful specialized knowledge. Pierce v. Quarterman, 2008 WL 4445064, at *18.
On this motion for COA, Pierce does not dispute that the applicable state rules of evidence required exclusion of the proffered testimony, but urges that due process nevertheless required the trial court to allow the jury to hear the testimony. Pierce cites Chambers v. Mississippi, 410 U.S. 284, 93 S.Ct. 1038, 35 L.Ed.2d 297 (1973), Green v. Georgia, 442 U.S. 95, 99 S.Ct. 2150, 60 L.Ed.2d 738 (1979), and Rock v. Arkansas, 483 U.S. 44, 107 S.Ct. 2704, 97 L.Ed.2d 37 (1987), for the proposition that a state’s evidentiary rules should not be applied to deprive Pierce of the ability to present a defense where the proffered evidence otherwise bears indicia of trustworthiness. But this mischaracterizes the holdings of these cases. The Supreme Court subsequently clarified, in Montana v. Egelhoff, 518 U.S. 37, 116 S.Ct. 2013, 135 L.Ed.2d 361 (1996), that Chambers and its progeny do not stand for the proposition “that a defendant is denied a fair opportunity to defend against the State’s accusations whenever critical evidence favorable to him is excluded,” but rather that “erroneous evidentiary rulings can, in combination, rise to the level of a due process violation.” Id. at 53,116 S.Ct. 2013 (internal quotation marks omitted). *791The Court specifically rejected the possibility that due process requires that “all competent, reliable evidence must be admitted.” Id. (internal quotations omitted). The state habeas court’s conclusion that the architect’s proposed testimony was inadmissible was a reasonable application of clearly-established Supreme Court law. The district court’s conclusion that the exclusion of the architect’s testimony did not provide a basis for habeas relief is not debatable.
C. The Jury Misconduct Claim
Pierce contends that the jury improperly considered extrinsic evidence and engaged in other acts of misconduct. He also contends that the district court erred in refusing to grant an evidentiary hearing on these issues. First, Pierce asserts that one juror improperly performed an out-of-court experiment during deliberations in order to evaluate the testimony of one of the eyewitnesses, Reginald Sanders, who testified that he saw Pierce’s reflection in a window of the Church’s Chicken as he went around a corner of the restaurant. The juror regularly ate breakfast at a cafeteria and confirmed, based on visual observations of the cafeteria window, that one could indeed see a reflection in a window before going around the corner. Second, Pierce contends that the jurors improperly considered Pierce’s failure to take the stand as evidence of his guilt. Finally, Pierce contends that the jury improperly consulted a dictionary to define the term “deliberate” in the first special issue. Pierce’s federal habeas petition attached signed affidavits by three of the jurors attesting to these facts. Although these affidavits were subscribed and sworn to in August and September 1990 (before Pierce filed his state habeas petition in December 1990), they were never presented to the state habeas court, and there was no other evidence before the state habeas court to establish a factual basis for Pierce’s assertions.
The state habeas court denied relief, concluding that Pierce had offered no proof to support his juror misconduct claims and, with one exception, had not named the jurors allegedly involved. The federal district court also denied relief, citing lack of proof: “Pierce points to no evidence supporting any of these claims.” Pierce v. Quarterman, 2008 WL 4445064, at *26. As Pierce points out in the motion for COA, the district court’s statement was incorrect—Pierce’s federal habeas petition attached the three juror affidavits swearing to the facts that he alleged. We nevertheless conclude that jurists of reason would not find the district court’s ultimate denial of relief debatable because Pierce’s affidavit evidence was procedurally barred.
This court has looked to the exhaustion requirements of 28 U.S.C. § 2254(b) in determining whether a federal district court may consider affidavit evidence offered for the first time in a federal habeas petition. Under § 2254(b),2 federal habeas petitioners must fully exhaust available state court remedies before proceeding in federal court. This court reviews de novo the legal question of whether a federal habeas petitioner has exhausted state court remedies. Smith v. Quarterman, 515 F.3d 392, 400 (5th Cir.2008). “The exhaustion requirement is satisfied when the substance of the federal habeas claim has been fairly presented to the highest state court.” Morris v. Dretke, 379 F.3d 199, 204 (5th Cir.2004). Affidavits presented for the first time in federal habeas proceedings may not contain new factual *792allegations and must supplement—as opposed to fundamentally alter—claims presented to the state court. Id. at 204-05. We conduct a fact- and case-specific exhaustion inquiry to determine whether additional evidence fundamentally alters or merely supplements the state petition. Id. at 205. “If the petitioner presents material evidentiary support for the first time in federal court, then he has not exhausted his state remedies.” Smith, 515 F.3d at 400 (citing Morris, 379 F.3d at 204-05).
Smith v. Quarterman, 515 F.3d at 403, presented certain facts similar to those in the present case. In Smith, we concluded that affidavits presented for the first time in the federal habeas petition were procedurally barred for failure to exhaust under § 2254(b). Id. We noted that the affidavits provided the first actual evidence in support of the petitioner’s claims that trial counsel had performed ineffectively by failing to present evidence that the plaintiff was abused as a child. The petitioner’s state habeas application, by contrast, “contain[ed] no evidence of child abuse other than the petitioner’s allegations.” Id. at 402. We concluded that by failing to submit the affidavits to the state habeas court, “Smith failed to allow the TCCA an opportunity to review the credibility of’ the affidavits and therefore “threatened] the state’s right to pass upon and correct alleged violations of its prisoners’ federal rights.” Id. (internal quotation marks omitted).
This court has also looked to 28 U.S.C. § 2254(e)(2), which governs the circumstances under which a district court may grant an evidentiary hearing on a state court prisoner’s federal habeas petition, to determine whether a district court may consider an affidavit submitted for the first time with a federal habeas petition. Where a state court prisoner “has failed to develop the factual basis of a claim in State court proceedings,” § 2254(e) restricts the availability of an evidentiary hearing to narrow circumstances that Pierce does not allege are present here.3
We addressed a set of facts similar to those in this case in Diaz v. Quarterman, 239 Fed.Appx. 886 (5th Cir.2007) (per curiam), which, though unpublished, is persuasive in its reasoning. In Diaz, the state habeas court denied relief on the petitioner’s claim that counsel provided ineffective assistance by failing to present the mitigating testimony of certain family members who were willing to testify at trial. The state habeas court emphasized that the petitioner made various allegations but did not “attach any type of affidavit or other form of factual support for his claim that some of his family members would have been willing to testify.” Id. at 887. The petitioner then sought federal habeas relief and filed, for the first time, a series of affidavits that provided evidentiary support for the factual allegations raised in the state habeas court. We affirmed the district court’s denial of habeas relief, concluding that the affidavits were *793barred by § 2254(e)(2) because they had not been raised during the state court proceedings, and that absent that evidence, there was no basis to rebut the state court’s finding that no evidence supported the petitioner’s ineffective assistance claim. We observed:
Pursuant to AEDPA, we must presume these factual determinations to be correct absent clear and convincing evidence to the contrary. The only evidence Diaz offers to rebut the state court’s findings is the series of affidavits presented for the first time to the district court.... [W]e cannot consider them per [28 U.S.C.] § 2254(e)(2), as they comprise “new evidence” that was not properly presented to the state court, and they do not evidence a factual predicate that could not have been discovered through the exercise of due diligence. Without the affidavits, Diaz has failed to rebut the presumption of correctness that attaches to the state court’s findings, and he cannot make his case that counsel were constitutionally ineffective at the punishment phase of trial.
Id. at 890 (emphasis added, citation omitted).
Pierce acknowledges that he failed to exhaust and to build an evidentiary record as to juror misconduct in the state habeas court but argues that this failure should be excused because he sought an evidentiary hearing from the state habeas court but never received one.4 But this argument ignores the fact that the affidavits that Pierce contends that the district court should have considered did not require an evidentiary hearing and were in fact available to him before his state habeas petition was filed. Under either § 2254(b) or § 2254(e)(2), the affidavits in support were procedurally barred at the district court level. Jurists of reason would not find the district court’s ultimate denial of relief on the issue of juror misconduct debatable.
For related reasons, we conclude that the district court did not abuse its discretion in refusing to grant an evidentiary hearing on the juror misconduct issue. As noted, except in narrow circumstances, § 2254(e)(2) bars an evidentiary hearing in the federal district court where the applicant has failed to develop a factual basis for the claim in the state habeas court. A failure to establish a factual basis is not established, however, “unless there is a lack of diligence, or some greater fault, attributable to the prisoner or the prisoner’s counsel.” Williams v. Taylor, 529 U.S. at 432, 120 S.Ct. 1479. Pierce argues that his failure to establish a factual basis is excused because he requested an evidentiary hearing in the state habeas court.
We rejected precisely this argument in Dowthitt v. Johnson, 230 F.3d at 758. In Dowthitt, as here, the petitioner urged that his failure to develop the factual basis for his habeas claims was excused under § 2254(e)(2) because he requested but was denied evidentiary hearings in the state habeas court. We disagreed, concluding that “[mjere requests for evidentiary hearings will not suffice; the petitioner must *794be diligent in pursuing the factual development of his claim.” Id. We observed that the petitioner had failed to present affidavits in the state habeas court from the witnesses that he claimed would provide material information and “did not show that they could not be obtained absent an order for discovery or a hearing.” Id. (internal quotation marks omitted). We concluded that the petitioner’s “proffers” to the state habeas court of what the witnesses would present at a hearing did not fulfill the diligence requirement, holding that “[g]iven that the [witnesses] were willing to testify at a hearing, [the petitioner] could easily have obtained their affidavits. A reasonable person in [petitioner’s place would have at least done as much.” Id. As in Dowthitt, we conclude that Pierce’s request for an evidentiary hearing was not enough to avoid the restrictions imposed by § 2254(e)(2). By failing to attach the juror affidavits, which were already in existence when he filed his petition in state habeas court, Pierce failed to take the proper steps to support a request for an evidentiary hearing in federal district court. The district court did not abuse its discretion in refusing to hold an evidentiary hearing.
D. The Atkins Claim
Pierce seeks a COA as to whether he is mentally retarded and therefore ineligible for execution under Atkins v. Virginia, 536 U.S. 304, 122 S.Ct. 2242, 153 L.Ed.2d 335 (2002). Pierce’s arguments focus almost exclusively on what Pierce describes as “new evidence” about the credibility of the State’s expert witness, Dr. George Denkowski, who evaluated Pierce in 2005 in connection with his state court habeas application. The TCCA refused to credit Dr. Denkowski’s testimony in another recent habeas case, Ex parte Plata, No. AP-75820, 2008 WL 151296 (Tex.Crim.App. Jan.16, 2008), due to several methodological errors. The Texas State Board of Examiners of Psychologists subsequently filed a complaint against Dr. Denkowski with the State Office of Administrative Hearings regarding his work in the Plata case, seeking to sanction him for intentionally misapplying psychiatric testing methods. See SOAH Docket No. 520-09-2282.
Pierce raises the following arguments in support of an evidentiary hearing and COA:
1. As in Plata, Dr. Denkowski improperly contended that depression and anxiety had a suppressive effect on Pierce’s IQ score;
2. As in Plata, Dr. Denkowski improperly evaluated Pierce’s adaptive deficits and overstated the impact of sociocultural factors on these deficits;
3. Dr. Denkowski improperly criticized the results of other IQ tests administered to Pierce as being less reliable because only certain subparts were administered;
4. Dr. Denkowski failed to inform the court of the “Flynn Effect,” which might have artificially inflated Pierce’s IQ score on tests administered in 1975 and 1976. Dr. Denkowski also failed to inform the court that these same tests may be structured so as to overrepresent IQ.
5. The state habeas trial court made clearly erroneous findings of fact about one of Pierce’s experts, Dr. Garnett, some of which were adopted by the TCCA in its denial of Pierce’s habeas application.
The district court arguably erred in concluding that none of these issues merited habeas relief or at least an evidentiary hearing. Accordingly, we grant a COA on the issues that Pierce raises with respect to his Atkins claim. Pierce is instructed to *795provide record cites that show where each such issue was raised before the state habeas court and federal district court— or, if the issue was not raised in these forums, to explain why the issue could not have been raised there.
E. The Ineffective Assistance Claim
Finally, Pierce seeks a COA as to whether his trial counsel performed deficiently during the sentencing phase by failing to investigate and present mitigating evidence that he was mentally retarded, abused as a child, and suffered an impoverished upbringing. Pierce also seeks an evidentiary hearing, arguing that such a hearing would conclusively establish deficiencies in counsel’s performance. Pierce argues that the state habeas court improperly denied such a hearing, and that because of this improper denial, the federal district court in turn abused its discretion in failing to hold an evidentiary hearing.
The district court held that Pierce’s ineffective assistance of counsel claim did not provide a basis for habeas relief because even if Pierce could show that his counsel performed deficiently, Pierce could not establish prejudice. Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), provides the two-prong standard for establishing ineffective assistance of counsel. First, the petitioner “must show that ... counsel made errors so serious that counsel was not functioning as the ‘counsel’ guaranteed by the Sixth Amendment.” Id. Second, the petitioner must “show that the deficient performance prejudiced the defense ... [with] errors [that] were so serious as to deprive the defendant of a fair trial, a trial whose result is rehable.” Id. The district court also noted the standard for establishing “prejudice” under the second prong: “[W]hether 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.
The district court concluded that even if counsel had in fact rendered deficient performance under the first prong, Pierce could not show prejudice under the second because the special issues posed to the jury at sentencing would not have permitted the jury to consider or give effect to the evidence that Pierce asserts should have been presented.5 The district court observed:
The evidence Pierce claims went undeveloped and unpresented—evidence of his low intelligence, his poor health as a child, the physical abuse he suffered at the hands of his father, the extreme poverty in which he grew up, and other evidence of a similar nature—is all general mitigation evidence, i.e., evidence that might have elicited sympathy or reduced his general moral culpability, but not evidence directly relevant to the special issues presented to the jury. As discussed ... in connection with Pierce’s Penny claim, the special issues provided the jury with no mechanism to consider or give effect to such general mitigation evidence.
Pierce v. Quarterman, 2008 WL 4445064, at *16. The district court held that “because the special issues provided no mechanism for the jury to give effect to such mitigating evidence, it cannot be said that *796there is a reasonable probability that such evidence would have changed the outcome.” Id.
The district court’s holding is debatable. Although the special issues would not have permitted the jury to give full effect to the types of mitigating evidence that Pierce contends should have been introduced,6 as we have held that Penry requires, see Nelson v. Quarterman, 472 F.3d 287, 316 (5th Cir.2006), the special issues were sufficient for the jury to give the evidence some effect. See, e.g., Coble v. Quarterman, 496 F.3d 430, 447 (5th Cir.2007) (observing that jury could give some effect to evidence of mental illness and a troubled background through deliberateness special issue); Tennard v. Dretke, 442 F.3d 240, 254 (5th Cir.2006) (noting that jury could give some effect to evidence of impaired intellectual functioning through deliberateness special issue); Lucas v. Johnson, 132 F.3d 1069, 1083 (5th Cir.1998) (concluding that jury could give some effect to evidence of schizophrenia and troubled upbringing through future dangerousness special issue). The district court’s conclusion—that the omitted mitigating evidence could not have prejudiced the outcome because the jury had “no mechanism” to give it effect—is therefore at least debatable. Pierce is entitled to a COA on this issue. Pierce may urge his entitlement to an evidentiary hearing as to ineffective assistance as part of his appeal.
The State contends that there is an independent basis for denying a COA on Pierce’s ineffective assistance claim: that Pierce’s counsel did not render ineffective assistance because the omission of the mitigating evidence was part of a sound trial strategy. In the state habeas court, Pierce’s lead counsel from his third trial testified by affidavit that he had properly investigated and was aware of the mitigating evidence but chose not to introduce it because he had pursued a theory of innocence and misidentification during the guilt/innocence phase and feared that he would lose credibility with the jury if he changed strategy to pursue a mitigation theory at sentencing. Pierce’s counsel introduced evidence as to lack of future dangerousness but avoided presenting evidence that would tend to admit but excuse the crime. The state habeas court found that Pierce’s counsel did not render ineffective assistance and had omitted the mitigating evidence as part of a “plausible trial strategy.”
The federal district court did not describe or address the state habeas court’s grounds for denying relief on the ineffective assistance claim. Therefore, on this motion for COA, we do not have the benefit of a district court finding as to whether the state habeas court’s conclusion was objectively unreasonable or a violation of clearly-established Supreme Court law. Nor has Pierce, whose motion for COA properly challenged only the district court’s conclusions, had the opportunity to brief the issue for this court. Accordingly, we do not decide at this time whether the state habeas court’s findings provide an independent basis for the denial of habeas relief. The State may reurge this argument in its appellate briefing.
IV. Conclusion
Pierce’s request for a COA is GRANTED as to the Atkins and ineffective assis*797tance of counsel claims. The parties are directed to submit supplemental briefing on these claims in advance of oral argument on a schedule to be established by the Clerk. Pierce’s request for a COA is otherwise DENIED. The State’s appeal of the district court’s grant of relief under Penry will be addressed after oral argument, during which we will hear argument as to Pierce’s Penry, Atkins, and ineffective assistance claims.
Pursuant to 5th Cir R. 47.5, the court has determined that this opinion should not be published and is not precedent except under the limited circumstances set forth in 5th Cir. R. 47.5.4.
. With respect to Judge Dennis’s dissent on the Brady issue, we provide a somewhat fuller treatment of the issues with respect to the Sanders boys' testimony.
First, we describe the trial record on the Sanders brothers’ testimony. Although only Reginald Sanders saw the crime being committed, both boys saw Pierce flee the scene. Reginald Sanders testified that although he did not know Anthony Pierce by name, he had seen him before around their housing project and in fact had seen Pierce earlier that day wearing the same distinctly-patterned shirt that he was wearing when fleeing the scene of the crime. When questioned by a police officer on the night of the crime, Reginald Sanders identified the shooter’s last name as Pierce but added that "I wasn't too sure about his first name because I never really met him and I thought his first name was James." George Sanders similarly testified that he had seen Pierce before in their housing project and that he recognized the shooter as "one of the Pierce brothers,” though he did not know his first name. When brought to the police *790station as witnesses shortly after the shooting, both boys identified Pierce's shirt as the shirt worn by the shooter. The district court concluded that in light of these identifications, made immediately after the shooting, together with the testimony of two additional eye witnesses who did not receive a reward, there was no reasonable probability that disclosure of the reward paid after Pierce’s trial would have changed the outcome of the trial.
Second, we address the "arguably suggestive lineup” which the dissent urges as a basis for concluding that the reward money could have had material impeachment value. The district court concluded with regard to a separate issue raised in Pierce's habeas petition that the lineup was not impermissibly suggestive under Simmons v. United States, 390 U.S. 377, 384, 88 S.Ct. 967, 19 L.Ed.2d 1247 (1968), and Pierce does not seek a COA to appeal this conclusion.
. Section 2254(b) provides, in relevant part, that the district court should not grant a writ of habeas corpus to a state prisoner unless “the applicant has exhausted the remedies available in the courts of the State.” 28 U.S.C. § 2254(b)(1)(A).
. Section 2254(e)(2) provides:
If the applicant has failed to develop the factual basis of a claim in State court proceedings, the court shall not hold an evidentiary hearing on the claim unless the applicant shows that—
(A) the claim relies on—
(i) a new rule of constitutional law, made retroactive to cases on collateral review by the Supreme Court, that was previously unavailable; or
(ii) a factual predicate that could not have been previously discovered through the exercise of due diligence; and
(B) the facts underlying the claim would be sufficient to establish by clear and convincing evidence that but for constitutional error, no reasonable factfinder would have found the applicant guilty of the underlying offense.
. The procedural disposition of the motion for evidentiary hearing was odd. Pierce filed the motion in January 1991, shortly after filing his state court habeas petition. Court documents reflect that the motion was still pending in November 1995, when Pierce sought new appointed counsel. There was virtually no further activity on the docket until November 2000, when both parties filed proposed findings of fact and conclusions of law. The record does not show that the state habeas court ruled on the motion before ruling on the proposed findings of fact and conclusions of law, but also does not show that Pierce’s counsel raised any objection to submitting proposed findings of fact and conclusions of law without a ruling on the pending motion.
. The special issues were:
1) Whether Pierce's conduct that caused Johnson's death was deliberate and undertaken with the reasonable expectation that the death of the victim or another would result; and
2) Whether there was a probability that Pierce would commit future criminal acts of violence that would constitute a continuing threat to society.
Tex.Code Crim. Proc. Ann., Art. 37.071(b) (Vernon 1981).
. See, e.g., Penry, 492 U.S. at 320, 109 S.Ct. 2934 (Texas special issues did not permit jury to consider and give full effect to evidence of mental retardation, childhood abuse); Tennard v. Dretke, 542 U.S. 274, 287, 124 S.Ct. 2562, 159 L.Ed.2d 384 (2004) (same, as to mental defect); Abdul-Kabir v. Quarterman, 550 U.S. 233, 259, 127 S.Ct. 1654, 167 L.Ed.2d 585 (2007) (same, as to difficult childhood, lack of self-control, and possible neurological damage); Brewer v. Quarterman, 550 U.S. 286, 296, 127 S.Ct. 1706, 1721-22, 167 L.Ed.2d 622 (2007) (same, as to childhood abuse).