JERRY E. SMITH, Circuit Judge:
Donell Jackson requests a certificate of appealability (“COA”) from the denial of his claim for federal habeas corpus relief under 28 U.S.C. § 2254. We deny a COA as to all but two of Jackson’s claims on which a COA is required, because jurists of reason would not find the rejection of them debatable. As for the claim on which we grant a COA, and the claim for which no COA is required, we affirm on the merits.
I.
Jackson was charged with killing his victim for remuneration. The victim had previously testified before a grand jury in its investigation of Jackson’s friend, David Smith. Smith indicated in a taped statement that he did not know Jackson was going to shoot the victim. When the police played Smith’s statement for Jackson during interrogation, Jackson allegedly replied that Smith had paid him to commit the murder. Jackson then made a taped confession. To shift the blame, Jackson at trial claimed the police had told him to say that Smith had paid him.
Jackson was convicted by a jury of capital murder. At sentencing, the state introduced evidence of prior offenses, and Jackson presented evidence of a favorable home life and a learning disability. The jury sentenced him to death, finding that he posed a threat of future dangerousness and that the mitigating evidence was inadequate to warrant a life sentence.
The Texas Court of Criminal Appeals affirmed the conviction and sentence on direct appeal. Jackson filed a concurrent petition for writ of habeas corpus in the trial court, which entered findings of fact and conclusions of law that were adopted by the Court of Criminal Appeals in an order denying habeas relief.
Jackson filed a federal habeas petition under § 2254, alleging twenty-two points of error. The district court granted summary judgment denying Jackson’s claims, and denied sun sponte a COA as to each claim. Jackson filed a notice of appeal and request for a COA.
II.
This case is governed by the Antiterrorism and Effective Death Penalty Act of 1996 (“AlEDPA”), which requires, as a jurisdictional prerequisite to appeal, that Jackson obtain a COA. Miller-El v. Cockrell, 537 U.S. 322, 335-36, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003). A COA will issue if Jackson makes “a substantial showing of the denial of a constitutional right.” 28 U.S.C. § 2253(c)(2). The prevailing standard requires Jackson to demonstrate that “reasonable jurists could debate whether (or, for that matter, agree that) the petition should have been resolved [by the district court] in a different manner or that the issues presented were ‘adequate to deserve encouragement to proceed further.’ ” Slack v. McDaniel, 529 U.S. 473, 484, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000) (quoting Barefoot v. Estelle, 463 U.S. 880, 893 n. 4, 103 S.Ct. 3383, 77 L.Ed.2d 1090 (1983)).
Athough the COA determination requires a threshold inquiry into the merits of a petitioner’s claim, it does not involve a full canvassing of the factual or legal bases for relief. See Miller-El, 537 U.S. at 336-37, 123 S.Ct. 1029. We do not inquire whether Jackson will succeed on appeal, or even whether any reasonable jurist would ultimately grant Jackson’s petition. Rath[404]*404er, we ask only whether the federal district court’s resolution of Jackson’s claims is debatable among jurists of reason.1
When assessing whether jurists of reason could debate the denial of Jackson’s habeas petition, we are mindful of the deferential standard of review the district court must apply under AEDPA. See Miniel v. Cockrell, 339 F.3d 331, 336 (5th Cir.2003). The district court must defer to the state court’s adjudication of a defendant’s claims on the merits unless the state court’s decision was “contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States, or ... 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), (2).
A state court’s decision is “contrary to” clearly established federal law if it reaches a result in direct conflict with Supreme Court precedent, either by drawing a contrary legal conclusion or basing a contrary judgment on materially indistinguishable facts. Miniel, 339 F.3d at 337 (citing Williams v. Taylor, 529 U.S. 362, 405, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000)). A state court’s decision is based on an “unreasonable application” of clearly established federal law if it is “objectively unreasonable.” Id. Therefore, it is not enough for the reviewing court to believe that the state court applied Supreme Court precedent incorrectly;2 rather, the application must be outside the range of reasonable judgment permitted by the particular rule.3
It is the ultimate legal conclusion reached by the state court, not every step of its reasoning process, that should be tested for unreasonableness. See Santellan v. Cockrell, 271 F.3d 190, 193 (5th Cir.2001). Finally, AEDPA presumes that the state court’s factual findings are correct; the defendant has the burden of proving otherwise by “clear and convincing evidence.” 28 U.S.C. § 2254(e)(1).
III.
Jackson makes eight separate arguments for a COA. We deal with each of these in turn.
A.
Jackson argues that his confession was involuntary and the product of police misconduct. Specifically, he maintains that, to shift blame to Smith, police told him to say that he received money for the victim’s murder; Jackson alleges that discrepancies between the details of his confession and statements made by Smith compel the conclusion that police coerced a confession.
The Fifth Amendment provides that no person “shall be compelled in any criminal case to be a witness against himself.” U.S. Const, amend. V. “[A] confession, in order to be admissible, must be free and voluntary: that is, must not be extracted by any sort of threats or violence, nor obtained by any direct or implied promises, however slight, nor by the exertion of any improper influence.” Bram v. United States, 168 U.S. 532, 542-43, 18 S.Ct. 183, [405]*40542 L.Ed. 568 (1897) (quoting 3 Russell on Crimes 478 (6th ed.)).
As the district court noted, the admissibility of Jackson’s confession might be in doubt if the facts he alleges were true. The jury, however, considered the evidence presented by Jackson and the police at trial, and found that no promises were made to Jackson in exchange for his confession. This credibility determination is squarely within the province of the jury,4 and AEDPA tells us to presume that this finding is correct unless rebutted by “clear and convincing evidence.” 28 U.S.C. § 2254(e)(1). Because Jackson did not present any new evidence in his habeas petition that would satisfy this rigorous standard, reasonable jurists could not disagree with the denial of a COA on this issue.
B.
Jackson contends that the alleged discrepancies between his confession and Smith’s statements prove that the confession is false, so there was no evidence to establish that Jackson killed the victim for remuneration. Hence, Jackson maintains that he is actually innocent of capital murder.
A claim of actual innocence based on newly discovered evidence is not cognizable for purposes of federal habeas corpus absent an independent constitutional violation. Herrera v. Collins, 954 F.2d 1029, 1034 (5th Cir.1992), aff'd, 506 U.S. 390, 113 S.Ct. 853, 122 L.Ed.2d 203 (1993). This rule recognizes that the purpose of federal habeas corpus is “to ensure that individuals are not imprisoned in violation of the Constitution — not to correct errors of fact.” Herrera, 506 U.S. at 399, 113 S.Ct. 853. A petitioner may prove actual innocence to overcome a procedural default, allowing a federal habeas court to reach the merits of an otherwise barred constitutional claim. Schlup v. Delo, 513 U.S. 298, 316, 115 S.Ct. 851, 130 L.Ed.2d 808 (1995).
Jackson does not allege actual innocence to remove a procedural bar to a separate constitutional claim. Rather, he submits evidence, consisting of testimonial discrepancies and expert opinion that he may suffer from a learning disability and other psychological problems, to diminish the probative value of his confession. He seeks only to remove the evidentiary basis of the jury’s conclusion that he committed capital murder; i.e., murder-for-hire. Because this is a free-standing actual innocence claim, no reasonable jurist could disagree that Jackson failed to make “a substantial showing of the denial of a constitutional right.” 28 U.S.C. § 2253(c)(2). Therefore, a COA for this claim is denied.
C.
1.
Jackson urges that the state exercised its peremptory challenges in a racially discriminatory manner, in violation of his Fourteenth Amendment rights under Batson v. Kentucky, 476 U.S. 79, 106 S.Ct. 1712, 90 L.Ed.2d 69 (1986). The Batson Court held that a defendant must first make a prima facie showing that the prosecutor is exercising his strikes based on the prospective juror’s race. See id. at 96-97, 106 S.Ct. 1712.
“Once the defendant makes a prima facie showing, the burden shifts to the State to come forward with a neutral explanation for challenging [minority] jurors.” Id. at 97, 106 S.Ct. 1712. If the state is unable to offer a race-neutral explanation, the defendant’s sentence should be reversed. See id. at 100, 106 S.Ct. 1712. If the state advances putatively neutral reasons, the defendant bears the ultimate burden of proving that those reasons are pretextual. See id. at 94 n. 18, 106 S.Ct. 1712.
[406]*406In Miller-El, the Court reversed this court’s denial of a COA on a Batson claim, finding that it was debatable among jurists of reason whether Miller-El would succeed in his federal habeas case. Miller-El, 537 U.S. at 348, 123 S.Ct. 1029. The Court noted that deference to the state court is often appropriate for Batson claims, because whether the defendant has carried his burden of proof will often turn on the credibility of the prosecutor exercising the strikes, and “a reviewing court, which analyzes only the transcripts from voir dire, is not as well positioned as the trial court is to make credibility determinations.” Id. at 339, 123 S.Ct. 1029. Such deference, however, does not mean that a COA shall never issue; rather, “[a] federal court can disagree with a state court’s credibility determination and, when guided by AED-PA, conclude the decision was unreasonable or that the factual premise was incorrect by clear and convincing evidence.” Id. at 340, 123 S.Ct. 1029.
Miller-El, therefore, did not alter the standards for evaluating requests for a COA under AEDPA, nor did it articulate a new test for reviewing Batson claims; rather, it spoke only to “the type and quantum of record evidence” needed to establish eligibility for a COA. Murphy v. Dretke, 416 F.3d 427, 439 (5th Cir.2005) (describing Miller-El v. Dretke, 545 U.S. 231, 125 S.Ct. 2317, 162 L.Ed.2d 196 (2005) (‘Miller-El II”)), cert. denied, — U.S. -, 126 S.Ct. 1028, 163 L.Ed.2d 868 (2006).
In Miller-El, the Court found a number of circumstances in the record that supported the Batson claim. To succeed on a Batson claim, however, a petitioner need not submit each type of evidence addressed by Miller-El. A petitioner is also not limited to the types of evidence eonsidered by the Court in Miller-El. There, the Court found the following factual circumstances persuasive in determining that a COA should issue:
(1) the State used 10 of its 14 peremptory strikes against African-Americans, and only one ultimately served on the jury;
(2) the trial court conducted a Batson hearing two years after voir dire, so the court had no occasion to judge the prosecutor’s credibility;
(3) the race-neutral reasons provided for striking certain black jurors applied equally well to white jurors who went unchallenged;
(4) the State used disparate questioning for white and black jurors, prefacing its questions to more than half the prospective black jurors with an explicit description of Texas’s execution procedures (compared to 6% of whites), and informed 94% of whites of the statutory minimum sentence (compared to 12.5% of blacks);
(5) the State requested a jury shuffle when a predominant number of African-Americans sat at the front of the panel; and
(6) evidence suggested that, historically, a culture of bias against African-American jurors suffused the District Attorney’s office, including the formal training of assistant district attorneys on how to exclude minorities from juries.
Miller-El, 537 U.S. at 342-47, 123 S.Ct. 1029.
To support his Batson claim, Jackson presents two types of evidence that are similar to the first and third circumstances examined in Miller-El. First, he points out that 5 of the 11 (or 45%) of the peremptory strikes were against black venire members.5 Second, he asserts that some of the race-neutral reasons provided [407]*407for striking certain black venire members applied equally to white venire members who went unchallenged and were selected for the jury. He also contends that the prosecutor’s reasons for striking the five black venire members were pretextual because the proffered reasons did not accurately reflect the voir dire testimony of the members.
The Court in Miller-El stated that, when the prosecution’s reasons for striking black jurors could apply equally well to white jurors who were ultimately empaneled, “the application of these rationales to the venire might have been selective and based on racial considerations.” Id. at 343, 123 S.Ct. 1029. In particular, the Court noted that similarly-situated white and black potential jurors expressed ambivalence about the death penalty. Id.
A COA determination under § 2253(c) requires “an overview of claims in the habeas petition and a general assessment of the merits.” Miller-El, 537 U.S. at 336, 123 S.Ct. 1029. This threshold inquiry, however, “does not require full consideration of the factual or legal bases adduced in support of a claim.” Id.
After our threshold inquiry into the merits of Jackson’s claim, we conclude that reasonable jurists could debate whether the state’s use of peremptory strikes against black venire members was race-based and thus in violation of Batson. We therefore grant a COA on this claim. After reviewing the briefs and record in full, however, we deny Jackson’s claim for habeas relief, finding the state habeas court’s determinations to be consistent with federal law as established by the Supreme Court.
2.
Jackson objects to the strikes of five black jurors — Maria Brooks, Lee Davis, Myrtle Gibson, Ingrid Poindexter, and Láveme Reid. We consider each of these briefly in turn.
The state indicated it struck Brooks because she stated she would have difficulty deciding that the state had proved future dangerousness;6 she expressed opposition to the death penalty; she said her religion taught her not to sit in judgment of another person. Though Jackson cites Terry Arnold as an example of a white juror who was empaneled despite expressing similar reservations about sitting in judgment of another,7 Arnold’s [408]*408reservations in this respect were less serious than were Brooks’s. Arnold also did not express hesitancy about being able to find future dangerousness.
The state’s reason for striking Davis was his apparent opposition to the death penalty and his indication that he would hold the prosecution to an elevated standard in capital cases.8 Jackson does not compare Davis to an empaneled white juror, but rather argues that Davis’s answers suggest he would be able to apply the correct burden of proof fairly in a capital case. Even though Davis softened his statement that he would require proof of guilt to a certainty, the state was entitled to conclude that he might require it to prove guilt by an elevated standard even if that burden were something less than metaphysical certainty.
The state claims it struck Gibson because she stated she believed that black people were treated unfairly by the criminal justice system, because she thought she might know the defendant personally, and because she was unsure about her feelings on the death penalty. Besides challenging these contentions on the merits, Jackson argues that Gibson’s comment about the unfair treatment of black people is substantially similar to white empaneled juror Kevin Chapman’s comment that the justice system treats marihuana users unfairly.9
d.
As for Poindexter, the state points [409]*409to strong language10 in her questionnaire opposing the death penalty and stating that life imprisonment is a worse punishment than death. Jackson again points to Chapman, who initially stated he would hold the state to a higher burden of proof in capital cases but later clarified that he understood that the applicable burden of proof was beyond a reasonable doubt in all cases.11
e.
Reid’s testimony suggested that she thought that to prove future dangerousness, the state would have to demonstrate that the defendant would commit murder in the future.12 She also expressed confusion over the special issues. Jackson argues that Reid equivocated in her testimony, that the state rushed Reid through her voir dire, and that empaneled juror Brian Summers indicated similar confusion on the special issues.13
Jackson also contends that the prosecutor’s reason for striking Reid based on the fact that she did not know that murder-for-hire was a capital offense, was similar to statements made by empaneled juror Chapman. Given the strong statements made by Reid concerning her reluctance to find future dangerousness, the state certainly had a valid race-neutral reason to use a peremptory challenge for Reid.
8.
AEDPA requires that the trial court’s decision be an “unreasonable application” of clearly established federal law or based on an “unreasonable determination” of the facts in light of the trial record. 28 U.S.C. § 2254(d)(1), (2). Jackson does not present substantial evidence of racial bias in jury selection beyond questionable distinctions in juror testimony. The trial court’s decision to permit the state to exercise its peremptory strikes as it did falls well within the “the range of reasonable judgment” afforded by AEDPA. See Yarborough, 541 U.S. at 664, 124 S.Ct. 2140. Therefore, Jackson’s request for habeas relief on this issue is denied.
[410]*410D.
Jackson contends that the trial court should have instructed the jury that any unadjudicated extraneous offenses introduced during the punishment phase needed to be proven beyond a reasonable doubt. Jackson relies on Apprendi v. New Jersey, 530 U.S. 466, 490, 120 S.Ct. 2848, 147 L.Ed.2d 435 (2000), which held that “[ojther than the fact of prior conviction, any fact that increases the penalty for a crime beyond the prescribed statutory maximum must be submitted to a jury, and proved beyond a reasonable doubt,” and Ring v. Arizona, 536 U.S. 584, 609, 122 S.Ct. 2428, 153 L.Ed.2d 556 (2002), which extended Apprendi to capital cases. Jackson’s claim is barred by the non-retroactivity principles of Teague v. Lane, 489 U.S. 288, 109 S.Ct. 1060, 103 L.Ed.2d 334 (1989), and at any rate, the state court’s refusal to deny a special instruction is not contrary to clearly established federal law as articulated by the Supreme Court. See 28 U.S.C. § 2254(d)(1). Therefore, we deny his request for a COA on that issue.
Under Teague, the relevant inquiry is “whether a state court considering [the defendant’s] claim at the time his conviction became final would have felt compelled by existing precedent to conclude that the rule [he] seeks was required by the Constitution.” Goeke v. Branch, 514 U.S. 115, 118, 115 S.Ct. 1275, 131 L.Ed.2d 152 (1995) (internal quotations omitted).14 Apprendi and Ring create new rules of constitutional law that are not retroactively applicable to cases under federal habeas review.15 Therefore, the only question left to answer is when Jackson’s conviction became final.
“A state conviction and sentence become final for purposes of retroactivity analysis when the availability of direct appeal to the state courts has been exhausted and the time for filing a petition for a writ of certiorari has elapsed or a timely filed petition has been finally denied.” Caspari v. Bohlen, 510 U.S. 383, 390, 114 S.Ct. 948, 127 L.Ed.2d 236 (1994). Jackson’s motion for rehearing was denied on June 9, 1999, so he had ninety days from that date to file a certiorari petition. See Sup.Ct. R. 13. On September 7,1999, therefore, Jackson’s conviction became final, the year before Apprendi was decided. Therefore, Teague bars Jackson’s claim.16
We note that even if Teague did not apply here, Apprendi and Ring would not provide Jackson with a legal basis for a COA. Ring states only that “[i]f a State makes an increase in a defendant’s authorized punishment contingent on the finding of a fact, that fact — no matter how the State labels it — must be found by a jury beyond a reasonable doubt.” Ring, 536 U.S. at 602, 122 S.Ct. 2428 (emphasis added).
The only fact capable of elevating Jackson’s charge to capital murder was proof of remuneration.17 The state introduced evi[411]*411dence of unadjudicated offenses only to prove future dangerousness in the sentencing phase, where the jury must exercise its discretion to decide whether to impose a death sentence or life imprisonment without parole.18
Therefore, Jackson invites us to answer the unresolved question whether Ring and Apprendi apply to any fact found by a jury that bears on its ultimate decision to impose death, or merely those facts that increase the authorized punishment to death. Because the trial court’s decision not to require such an instruction is not contrary to clearly established Supreme Court precedent, we would in any event deny a COA.
Similarly, Jackson asserts that the mere admission of evidence of unadjudicated, extraneous offenses violates his rights under the Eighth and Fourteenth Amendments and justifies a COA. Because Jackson cites no authority specifically for this proposition, the argument is waived for inadequate briefing.19
Even if the argument were not waived, Jackson would not be entitled to a COA. If he cannot prove that a COA should issue as to whether unadjudicated extraneous offenses need to be proven beyond a reasonable doubt, then a fortiori he cannot prove that a COA should issue as to whether such offenses are per se inadmissible. Because he does not point to any Supreme Court precedent foreclosing the trial court’s decision to permit evidence of unadjudicated extraneous offenses, he cannot make a substantial showing of a denial of a constitutional right.20
F.
Jackson claims that he deserves a COA because the trial court refused, in violation of his Eighth and Fourteenth Amendment rights, to instruct the jury that failure to reach a verdict on either of two special issues would automatically result in a life sentence. The Texas Code of Criminal Procedure provides that if the jury is unable to answer a special issue unanimously in the affirmative or negative, “the court shall sentence the defendant to confinement in the institutional division of the Texas Department of Criminal Justice for life imprisonment without parole.” Tex.Code Crim. Proc. art. 37.071 § 2(g). The Code also provides, however, that “[t]he court, the attorney representing the state, the defendant, or the defendant’s counsel may not inform a juror or a prospective juror of the effect of a failure of a jury to agree on [special] issues[.]” Id. at § 2(a). Jackson maintains that this provision violates the Eighth and Fourteenth Amendments by failing to inform a capital sentencing jury of relevant state sentencing law.
[412]*412This claim is without merit. In Jones v. United States, 527 U.S. 373, 381-82, 119 S.Ct. 2090, 144 L.Ed.2d 370 (1999), the Court held that the Eighth Amendment does not require a court to instruct a capital jury about the consequences of deadlock. The Court noted that the Eighth Amendment requires that a death sentence not be arbitrarily imposed, id. at 381, 119 S.Ct. 2090, but rejected the argument that “a death sentence is arbitrary within the meaning of the Eighth Amendment if the jury is not given any bit of information that might possibly influence an individual juror’s voting behavior,” id. at 382, 119 S.Ct. 2090. Because Jones controls, reasonable jurists would not disagree with the district court’s resolution of this issue. We deny a COA on this question.
G.
Jackson alleges the trial court violated his Eighth Amendment rights by failing to instruct the jury that it could consider mitigating evidence even if it did not relate to moral blameworthiness. Specifically, Jackson argued at the punishment phase that the jury should receive the following instruction:
The term “mitigating” evidence or “mitigating” factor as used herein means any type of evidence relating to the defendant’s background, character or the circumstances of the crime that would militate in favor of a life sentence rather than a death sentence. Evidence may be mitigating even if it does not relate in any way to the defendant’s moral culpability or moral blameworthiness for the capital murder listed in the indictment.
Instead, the court gave the following instruction (in relevant part):
A mitigating circumstance may include, but is not limited to, any aspect of the defendant’s character, background, record, emotional instability, intelligence or circumstance of the crime which you believe could make a death sentence inappropriate in this case.... In answering Special Issue No. 2 you shall consider mitigating evidence to be evidence that a juror might regard as reducing the defendant’s moral blameworthiness, including evidence of the defendant’s background, character, record, emotional instability, intelligence, or the circumstance of the offense that mitigates against the imposition of the death penalty.
Jackson apparently reasons that, by merely including background, character, and circumstances of the offense as modifiers of the general category of moral blameworthiness, instead of expressing these criteria in the conjunctive, the state unconstitutionally limited the scope of the mitigating instruction for Special Issue 2.
The Texas Code of Criminal Procedure provides that the court shall instruct the jury (should the jury make certain preliminary findings) that it shall consider “all of the evidence, including the circumstances of the offense, the defendant’s character and background, and the personal moral culpability of the defendant,” in determining whether a defendant should receive life without parole instead of death. Tex. Code Crim. Proc. art. 37.071 § 2(e)(1). Later, however, the Code defines “mitigating evidence” for purposes of this section as “evidence that a juror might regard as reducing the defendant’s moral blameworthiness.” Id. § 2(f)(4).
Relevant mitigating evidence must be within the “effective reach” of the jury during punishment. Johnson v. Texas, 509 U.S. 350, 368, 113 S.Ct. 2658, 125 L.Ed.2d 290 (1993) (internal quotation omitted). “[I]n a capital case, the sentencer must ... be able’to consider and give effect to [mitigating] evidence in imposing [a] sentence, so that the sentence imposed ... reflects a reasoned moral response to [413]*413the defendant’s background, character, and crime.” Penry v. Johnson, 582 U.S. 782, 788, 121 S.Ct. 1910, 150 L.Ed.2d 9 (2001) (internal quotations omitted). The sentencing instructions must provide the jury with an adequate vehicle to consider Jackson’s evidence and come to a reasoned moral conclusion. See id. at 800, 121 S.Ct. 1910.
The trial court’s determination that the instructions were constitutionally adequate is not “contrary to” clearly established federal law as articulated by the Supreme Court. In fact, in Johnson the Court approved of a mitigating instruction under the predecessor statute to the current provisions of the Texas Code that was less specific in its articulation of the relevant mitigating factors:
In determining each of these [Special] Issues, you may take into consideration all the evidence submitted to you in the trial of this case, whether aggravating or mitigating in nature, that is, all the evidence in the first part of the trial when you were called upon to determine the guilt or innocence of the Defendant and all the evidence, if any, in the second part of the trial wherein you are called upon to determine the answers to the Special Issues.
Johnson, 509 U.S. at 355, 113 S.Ct. 2658.
Neither was the instruction an “unreasonable application” of clearly established federal law. In Beazley v. Johnson, 242 F.3d 248, 260 (5th Cir.2001), we held that the current statute “does not unconstitutionally ‘preclude[ ] [the jury] from considering, as a mitigating factor, any aspect of a defendant’s character or record and any of the circumstances of the offense that the defendant proffers as a basis for a sentence less than death’ ” (citing Lockett v. Ohio, 438 U.S. 586, 604, 98 S.Ct. 2954, 57 L.Ed.2d 973 (1978)). We noted that the definition of mitigating evidence in § 2(f)(4) does not put any relevant evidence beyond the effective reach of the jury, because “[v]irtually any mitigating evidence is capable of being viewed as having some bearing on the defendant’s ‘moral culpability’ apart from its relevance to the particular concerns embodied in the Texas special issues.” Id. (citing Graham v. Collins, 506 U.S. 461, 476, 113 S.Ct. 892, 122 L.Ed.2d 260 (1993)).
This circuit has declined to articulate a precise test for what qualifies as “objectively unreasonable” under AEDPA.21 Where, however, a state court reaches a conclusion consistent with this circuit’s precedent, it presumptively falls within the broad discretion afforded the state court under § 2254(d)(1), because we presumably would consider our own case law as within “the range of reasonable judgment” afforded by Supreme Court decisions. See Yarborough, 541 U.S. at 664, 124 S.Ct. 2140.
Furthermore, the trial court could reasonably have concluded that the mitigating evidence offered by Jackson — that he was loved and admired by his family, assisted his grandmother, and provided help at his church and Sunday school — all sufficiently related to his “moral blameworthiness” as to come within the effective reach of the jury. Therefore, reasonable jurists could not disagree with the district court’s application of AEDPA’s deferential “unreasonable application” standard to Jackson’s claim. We deny a COA on this issue.
H.
Jackson avers that he is entitled to a COA because the district court denied his [414]*414motion for appointment of an expert in false confessions to support his claim that his confession was coerced and therefore inadmissible. Where expert services are “reasonably necessary” to mount a defense in a post-conviction proceeding, the district court may authorize the defense attorneys to obtain such services and shall pay the relevant expenses. 21 U.S.C. § 848(q)(9).22 Jackson argues that expert assistance was reasonably necessary because the circumstances surrounding the police interviews of Jackson and Smith raised a question as to the existence of remuneration. Specifically, when the police first interviewed Smith, he made no mention of paying Jackson for the murder. Only after Jackson confessed were police able to establish remuneration by further questioning Smith.
The state responds by noting that ruling on a motion to provide expert assistance is within the discretion of the district court. Hill v. Johnson, 210 F.3d 481, 487 (5th Cir.2000). Also, the state argues that any testimony rendered by the expert would be procedurally barred in a federal habeas proceeding because it was never presented in state court. Finally, because the jury’s credibility determination is entitled to a presumption of correctness, Jackson has not presented evidence to rebut that presumption and make necessary the appointment of an expert.
A COA is not required to appeal the denial of funds for expert assistance. Hill, 210 F.3d at 487 n. 3. Therefore, we may review the claim on direct appeal for abuse of discretion. Id. at 487. We will uphold a denial of funding where the petitioner has “(a) failed to supplement his funding request with a viable constitutional claim that is not procedurally barred, or (b) when the sought-after assistance would only support a meritless claim, or (c) when the sought after assistance would only supplement prior evidence.” Smith v. Dretke, 422 F.3d 269, 288 (5th Cir.2005) (internal citations omitted).
The district court did not abuse its discretion. At trial, Jackson testified that the police told him to confess that Smith paid him for murder in exchange for a lesser charge. The defense also presented two expert witnesses who testified that Jackson had a learning disability and was below average in intelligence, and that Jackson was prone to self-deprecation and other antisocial behaviors. Therefore, the testimony of a false confession expert would merely have supplemented other evidence already available to and considered by the jury. See id. at 288-89 (finding no abuse where expert testimony would merely reinforce testimony already given by defendant).
Even if we were inclined to agree as an initial matter that a false confession expert’s testimony was reasonably necessary for Jackson’s defense, the relevant statute vests discretion squarely in the district court.23 Therefore, we affirm the denial of Jackson’s motion for expert assistance.
[415]*415For the above reasons, Jackson’s request for a COA is GRANTED in part and DENIED in part. The judgment on the issue on which we grant a COA, and on the claim for which no COA is required, is AFFIRMED.
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.