JERRY E. SMITH, Circuit Judge:

LeJames Norman petitioned for a federal writ of habeas corpus raising two claims of ineffective assistance of counsel ("IAC") and requesting an evidentiary hearing to develop his claims. The district court denied Norman's petition and request and sua sponte denied a certificate of appealability ("COA"). Norman requests a COA from this court on three issues. We deny that motion.

I.

The district court summarized the details of the triple murder as follows, based on Norman's testimony at his accomplice's capital-murder trial.

Norman v. Stephens, No. V-12-054, 2015 WL 5732122, at *2 (S.D.Tex. Sept. 30, 2015).

Police arrested Ramey, but Norman fled to Mexico. Border Patrol officers arrested Norman as he crossed back into Texas using false identification.

Norman cooperated with law enforcement. He gave three recorded statements and testified before the grand jury, which, in 2006, indicted him for capital murder. Norman testified in 2007 at Ramey's capital-murder trial.

Given his confession and the extensive evidence implicating him in the murders, Norman pleaded guilty. The jury thus had to decide only life imprisonment or execution. In Texas, a jury imposes a sentence of death only by answering affirmatively two special-issue questions: (1) whether "from the evidence beyond a reasonable doubt . . . there is a probability that the defendant would commit criminal acts of violence that would constitute a continuing threat to society"; and (2) whether, after "[t]aking into consideration all of the evidence including the circumstances of the offense, the defendant's character and background, and the personal moral culpability of the defendant," "there is a sufficient mitigating circumstance or circumstances to warrant that a sentence of life imprisonment rather than a death sentence be imposed[.]" Id. at *3.

The state presented testimony and evidence demonstrating Norman's escalating history of criminality. At age ten, he committed two robberies on the same day using a firearm. In later years, he committed burglaries, criminal trespass, criminal mischief, using and selling drugs, and assault. At age nineteen, he committed the triple murder at issue here. Then, while on the run from law enforcement, he sold drugs, and while in county jail awaiting trial for capital murder, he made weapons, planned escapes, and talked about murdering people. During an unsuccessful escape attempt, Norman held a shank to the neck of a sixty-three-year-old jailer and threatened to kill her.

The defense focused on the two special issues. It claimed that Norman would not be a future danger and that mitigating circumstances warranted a life sentence. In support, the defense pointed to Norman's cooperation with police—his confessions, grand jury testimony, and testimony at Ramey's trial. It stressed how, in pre-indictment statements, Norman accepted responsibility and displayed remorse. And it presented testimony from twenty-one witnesses, including family members, friends, a coach, and teachers, and Norman's testimony, which he gave against the advice of counsel.

That testimony provided details into Norman's troubled childhood. His family was low-income and for a time lived in homeless shelters. His parents fought constantly, including physically, abused drugs and alcohol, sold drugs, associated with gang members, and abused Norman physically. When Norman was young, a police officer shot and killed his father. That incident greatly affected Norman, who was close to his father. In school, Norman attended special education classes. During high school, he fathered three children, whom witnesses say he loved and treated well.

In preparation for the sentencing phase, Norman's first set of attorneys hired at least two psychologists: Jack Greeson and Mark Cunningham. Greeson conducted extensive interviews with Norman's family and may have performed a psychological examination. Cunningham, on the other hand, only conducted a face-to-face interview with Norman, in county jail, lasting four hours twenty-eight minutes. Neither expert testified at any proceeding.

After Norman's lead counsel withdrew, the court appointed Allen Tanner, who secured the services of Micki Perry, a mitigation investigator. Perry recommended that Norman be evaluated by an expert in neuropsychology because Norman "was exposed to an extraordinary level of violence as a child," and "[t]here was a possibility of trauma to Mr. Norman's brain." Id. at *6.

Thereafter, Tanner retained Mohammed Hamza, a neuropsychologist. But because Hamza was unavailable to perform an examination, Tanner had Hamza's office partner, Curt Wills, perform a psychological examination. Wills was a clinical psychologist who did not have sufficient training to qualify as an expert in neuropsychology. He observed only "mild to moderate impairment" and "an indication of significant psychopathology." Id. He did not diagnose any significant neuropsychological or psychological problem. Tanner chose not to call Wills as a witness because his overall testimony would have been detrimental to Norman's case.

II.

After the sentence was affirmed, Norman sought collateral relief in state court. Through new, state-appointed postconviction counsel, he raised six grounds of relief, including IAC. One of the IAC claims was that trial counsel failed properly to investigate and present mitigation evidence that Norman suffered from a chemical brain imbalance. Norman, however, did not support that allegation with evidence of an imbalance.

The state courts denied the habeas petition, concluding that trial counsel had acted diligently and had decided, as a matter of trial strategy, not to have Wills testify. Relying on an affidavit by Tanner, who had served as trial counsel, the state courts mistakenly referred to Wills as a neuropsychologist.

While the state habeas action was pending, Norman filed a pro se "Motion for Leave to File Amended Notice of Appeal," which the state courts characterized as an attempt to file a successive state habeas application. On the same day that it denied his first application, the Court of Criminal Appeals denied Norman's motion. Ex parte Norman, No. WR-74,743-01 (Tex. Crim.App.2012) (unpublished).

Norman then filed the instant federal habeas petition. After the district court had authorized the use of $10,000 for Norman to retain a neuropsychological expert, Norman filed an amended petition that advanced two theories, only one of which is before us: that trial counsel's representation fell below constitutional requirements under Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), by failing to follow Perry's recommendation to hire a neuropsychological expert. The district court denied the amended petition because the claim was unexhausted and procedurally barred and, in the alternative, because it lacked merit.

The district court then sua sponte declined to issue a COA. Norman requests a COA from this court on three issues: (1) "Whether Reasonable jurists could disagree that the District Court should have conducted an Evidentiary Hearing"; (2) "Whether Reasonable jurists could disagree over whether the District Court Applied an incorrect standard of review in evaluating Nr. [sic] Norman's claims of ineffective post conviction counsel"; and (3) "Whether reasonable jurists could disagree that Mr. Norman received the effective assistance of counsel at trial." Motion for COA at 7.

III.

Norman maintains that reasonable jurists could disagree over whether the district court applied an incorrect standard of review in evaluating his claim of ineffective assistance of postconviction counsel. Norman would like to appeal that issue because, as explained below, he procedurally defaulted his claim of ineffective assistance of trial counsel in state court and thus must prove ineffective assistance of state postconviction counsel before a federal court may hear his habeas claim on the merits.

A COA may issue "only if the applicant has made a substantial showing of the denial of a constitutional right." 28 U.S.C. § 2253(c)(2). For constitutional claims rejected on the merits, the petitioner meets this test by "demonstrat[ing] that reasonable jurists would find the district court's assessment of the constitutional claims debatable or wrong." Slack v. McDaniel, 529 U.S. 473, 484, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000). Where, as here, claims are dismissed on procedural grounds, the petitioner must show both "[1] that jurists of reason would find it debatable whether the petition states a valid claim of the denial of a constitutional right and [2] that jurists of reason would find it debatable whether the district court was correct in its procedural ruling." Id. Norman has failed to make the requisite showings.

In state court, Norman raised a claim under Washington, alleging that trial counsel had provided ineffective assistance in not investigating and presenting expert testimony that he suffered from a chemical imbalance. But Norman did not allege that counsel provided ineffective assistance by failing to hire a neuropsychologist. The district court thus concluded that the claim was both unexhausted and procedurally defaulted,1 and Norman does not dispute that decision.

Under the independent-and-adequate-state-ground doctrine, federal district courts generally cannot review statecourt judgments that rest on an independent and adequate state ground, such as a state procedural default. Coleman v. Thompson, 501 U.S. 722, 729, 111 S.Ct. 2546, 115 L.Ed.2d 640 (1991). Norman nevertheless claims an exception to that rule. A petitioner overcomes a state procedural default where he can show "[1] cause for the default and [2] actual prejudice as a result of the alleged violation of federal law. . . ." Id. at 750, 111 S.Ct. 2546.2 Norman contends that he can make both showings. He maintains that his state postconviction counsel's ineffective assistance constitutes cause and that the default prejudiced him. He thus seeks a COA on the district court's contrary determination, specifically on the standard that the court used to reject his notion that he can overcome the state procedural default.

The district court chose to treat the procedural-default and merits issues together because "Norman's arguments to overcome the procedural bar implicate, and in fact merge with, a review of the substantive merits of his [Washington] claims." Norman, 2015 WL 5732122, at *12. The court's conflation of those issues makes it more difficult to follow its analysis. But, as we explain, we agree with the state that the court was correct in concluding that procedural default bars review of Norman's claim of ineffective assistance of trial counsel and that reasonable jurists could not disagree.

A.

Norman maintains that he had cause for his state procedural default because state postconviction counsel provided IAC in not raising the neuropsychologist issue in state court. Although an attorney's errors in a postconviction proceeding generally do not qualify as cause to excuse a default, Coleman, 501 U.S. at 752-53, 111 S.Ct. 2546, the Supreme Court has created an exception. In Martinez v. Ryan, ___ U.S. ___, 132 S.Ct. 1309, 182 L.Ed.2d 272 (2012), it held that a prisoner may establish cause for a default of an ineffective-assistance-of-trial-counsel claim in an "initial-review" collateral proceeding, i.e., a collateral proceeding in which the prisoner is able to raise the IAC claim for the first time. He must show both that the "appointed counsel in the initial-review collateral proceeding, where the claim should have been raised, was ineffective under the standards of [Washington]. . ." and that "the underlying ineffective-assistance-of-trial-counsel claim is a substantial one, which is to say that the prisoner must demonstrate that the claim has some merit." Id. at 1318. In Trevino v. Thaler, ___ U.S. ___, 133 S.Ct. 1911, 185 L.Ed.2d 1044 (2013), the Court held that Texas's procedural regime was similar to the one in Martinez because Texas's scheme rendered it almost impossible to raise IAC claims on direct appeal. The Court therefore extended Martinez's exception to Texas: The lack of effective counsel during initial state collateral-review proceedings can excuse procedural default on an IAC claim. Id. at 1921.

Norman fails to satisfy Martinez's and Trevino's test for establishing cause. Under those decisions, Norman may show cause for his default by demonstrating that his underlying ineffective-assistance-of-trial-counsel claim is substantial and that his state postconviction counsel was ineffective under Washington. The problem for Norman, however, is that his claim of ineffective assistance of trial counsel is not substantial.

To demonstrate that it is substantial, Norman would have to show that he might be able to satisfy Washington, 466 U.S. at 687, 104 S.Ct. 2052, which requires a prisoner to prove both deficient performance and actual prejudice. He demonstrates deficient performance by "showing that counsel made errors so serious that counsel was not functioning as the `counsel' guaranteed the defendant by the Sixth Amendment." Id. "Judicial scrutiny of counsel's performance must be highly deferential[,]" id. at 689, 104 S.Ct. 2052, and must consider "whether counsel's assistance was reasonable considering all the circumstances[,]" id. at 688, 104 S.Ct. 2052. The prisoner demonstrates actual prejudice by "showing that counsel's errors were so serious as to deprive the defendant of a fair trial [or a fair capital sentencing proceeding]. . . ." Id. at 687, 104 S.Ct. 2052.3 Except where there is a conflict of interest, a prisoner generally must "affirmatively prove[ ] prejudice." Id. at 693, 104 S.Ct. 2052. The proof need be only to a "reasonable probability" rather than satisfying the more stringent "more likely than not" standard. Id. at 693-94, 104 S.Ct. 2052.4

Norman fails to satisfy Washington because he cannot demonstrate actual prejudice. Mayfield's conclusions were largely cumulative of the testimony already adduced at trial. The defense had presented information on Norman's IQ, learning disabilities, deficits in reading and writing, and troubled childhood, including his parents' drug-dealing and abusive behavior and his father's death at the hands of police. The only part of Mayfield's report that was not already before the jury was her conclusion that Norman's tested abilities "were within normal limits." Mayfield did not diagnose Norman with any neurological or psychological disorder and did not report any childhood trauma or injury. Consequently, even if trial counsel was ineffective in not procuring a neuropsychologist, the allegedly deficient performance did not prejudice Norman.5

B.

Even if Norman could demonstrate cause for his procedural default, under Coleman the default would still preclude federal review unless he demonstrated actual prejudice, which he has not done. As already discussed, he cannot show that counsel's failure to procure a neuropsychological expert witness prejudiced him under Washington. He is thus likewise unable to demonstrate actual prejudice to overcome his state procedural default.

IV.

Norman requests a COA on "[w]hether reasonable jurists could disagree that Mr. Norman received the effective assistance of counsel at trial[.]" In other words, Norman seeks a COA to appeal the merits of his habeas claim, which, despite the procedural default, the district court ruled on as an alternative basis for denying Norman's petition.

As explained above, reasonable jurists would not disagree with the district court's procedural ruling. Consequently, the court's merits determination is moot and may not be appealed. We deny a COA on the third issue.

V.

Norman claims the district court should have conducted an evidentiary hearing. Under the Anti-Terrorism and Effective Death Penalty Act of 1996 ("AEDPA"), a state prisoner must obtain a COA before he can appeal the denial of a habeas petition. 28 U.S.C. § 2253(c)(1)(A). No similar requirement, however, exists for an appeal from the denial of an evidentiary hearing. We thus construe Norman's request for a COA on this issue as a direct appeal from the denial of an evidentiary hearing.

In habeas appeals, "a petition challenging an evidentiary ruling may only be entertained as corollary to a constitutional violation." Alix v. Quarterman, 309 Fed.Appx. 875, 878 (5th Cir.2009) (per curiam). Because we have determined that Norman's constitutional claims fail, we do not address the merits of his request for an evidentiary hearing. If we were to do so, however, we would deny it.

When 28 U.S.C. § 2254(e)(2) applies, the court cannot grant an evidentiary hearing unless the prisoner shows, first, that "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, second, that "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." 28 U.S.C. § 2254(e)(2). Norman has made no attempt to demonstrate that he satisfies these two criteria. Consequently, the provision bars an evidentiary hearing unless § 2254(e)(2) fails to apply to the claims of IAC.

Section 2254(e)(2) applies "[i]f the applicant has failed to develop the factual basis of a claim in State court proceedings[.]" In Williams v. Taylor, 529 U.S. 420, 432, 120 S.Ct. 1479, 146 L.Ed.2d 435 (2000), the Court interpreted the phrase "failed to develop" as meaning "lack of diligence, or some greater fault, attributable to the prisoner or the prisoner's counsel." A prisoner, the Court held, has not failed to develop the factual basis of a claim in state court just because "his diligent efforts to perform an act are thwarted, for example, by the conduct of another or by happenstance." Id.

Norman does not satisfy Williams, because his claims, by their very nature, are premised on the failure of "the prisoner's counsel" to develop the factual basis of the claims in state court. Id. But Norman urges us to follow Sasser v. Hobbs, 735 F.3d 833, 853 (8th Cir.2013), which interpreted Williams as standing more broadly for the proposition that failure to comply with § 2254(e)(2) can be excused if the failure was for "cause," such as, specifically, ineffectiveness of postconviction counsel.

Norman also points to Dickens v. Ryan, 740 F.3d 1302 (9th Cir.2014) (en banc), which created an exception to § 2254(e)(2) under a different theory. The court reasoned that § 2254(e)(2)'s procedural bar against the granting of a hearing applies only to evidentiary hearings on claims for "relief," which the court distinguished from evidentiary hearings "to show `cause' under Martinez." Id. at 1321. A petition for habeas relief—here the claim that trial counsel provided IAC—is a constitutional claim. See id. In contrast, a contention that postconviction counsel provided IAC under Martinez is merely equitable in nature. Id. (citing Martinez, 132 S.Ct. at 1319-20).

We need not decide whether we may grant an evidentiary hearing if there was "cause" for a procedural default within the meaning of Martinez and Trevino, because, as explained above, Norman cannot overcome the default of his underlying ineffective-assistance-of-trial-counsel claim. Because "the district court retains discretion over the decision to grant an evidentiary hearing once a petitioner overcomes the barriers presented by § 2254(e)(2)[,]" Clark v. Johnson, 202 F.3d 760, 765 (5th Cir.2000), we may impose other requirements, before granting an evidentiary hearing, in addition to the ones set forth in § 2254(e)(2).

A district court may refuse an evidentiary hearing where there is not "a factual dispute which, if resolved in [the prisoner's] favor, would entitle him to relief." Id. at 766. Because that is the situation here, the court did not abuse its discretion in denying a hearing. Norman has been granted both time and funding to develop his IAC claim for failure to hire a neuropsychologist, but he still has been unable to adduce any favorable mitigating evidence. The state did not challenge Mayfield's report or its findings but, instead, accepted the report and urged that Norman's petition be rejected, notwithstanding that new evidence. The district court agreed with the state's position, as do we. The denial of an evidentiary hearing was correct.

The application for a COA and the request for an evidentiary hearing are DENIED.