Before SMITH, COSTA, and HO, Circuit Judges. JERRY E. SMITH, Circuit Judge: Jamaal Howard, a Texas death-row inmate, moves for a certificate of appealability (“COA”) to contest the denial of his petition for a writ of habeas corpus. Because reasonable jurists would not dispute the issues, we deny the motion. I. After a jury deemed Howard competent to stand trial, another jury convicted him of capital murder.[1] Based on the jury’s answers to the special issues, the trial judge sentenced Howard to death. Howard filed a state habeas application raising a bevy of claims, including the ineffective-assistance-of-counsel (“IAC”) ones pressed in this motion. As relevant, Howard complained that his lawyer had failed to investigate and proffer evidence of his mental illness that would have (1) resulted in a life instead of death sentence; (2) persuaded the jury that he was incompetent to stand trial; and (3) shown that his Miranda waiver was neither knowing nor intelligent. The trial court recommended denying relief. The TCCA agreed. See Ex parte Howard, No. WR-77,906-01, 2012 WL 6200688, at *1 (Tex. Crim. App. Dec. 12, 2012) (per curiam) (unpublished). Howard petitioned for federal habeas, raising the same claims.[2] The dis-trict court declined to issue the writ, holding that, though Howard had ex-hausted the claims, he had failed to show that the state courts unreasonably applied federal law. See 28 U.S.C. § 2254(d). Now Howard seeks a COA.[3] II. Howard deserves a COA only if he “has made a substantial showing of the denial of a constitutional right.” 28 U.S.C. § 2253(c)(2). He satisfies that standard by demonstrating that his application involves issues that are debatable among jurists of reason, that another court could resolve the issues differently, or that the issues are suitable enough to deserve encouragement to proceed further.[4] “A court of appeals should limit its examination at the COA stage to a threshold inquiry into the underlying merit of the claims, and ask only if the District Court’s decision was debatable.” Buck v. Davis, 137 S. Ct. 759, 774 (2017) (cleaned up). Because Howard sits on death row, we resolve doubts in favor of issuing a COA. See, e.g., Hernandez v. Johnson, 213 F.3d 243, 248 (5th Cir. 2000). To prove IAC, Howard must show that counsel’s performance was objectively unreasonable and prejudiced him. Strickland v. Washington, 466 U.S. 668, 687–88, 694 (1984). Courts strongly presume that the performance was good enough. Rockwell v. Davis, 853 F.3d 758, 761 (5th Cir. 2017). “[C]ounsel has a duty to make reasonable investigations or to make a reasonable decision that makes particular investigations unnecessary.” Washington, 466 U.S. at 691. “[A] particular decision not to investigate must be directly assessed for reasonableness in all the circumstances,” but we still “apply[] a heavy measure of deference.” Id. A lawyer’s work can be deficient where he fails, at the punishment phase, to look into and present mitigating evidence of the defendant’s life history or mental illness.[5] Because Howard exhausted the relevant claims, the district court’s job was to determine whether the state adjudications were contrary to, or unreasonably applied, clearly established federal law as determined by the Supreme Court, or unreasonably determined the facts. See 28 U.S.C. § 2254(d)(1)–(2). So, in this posture, we ask whether it’s debatable that “there is any reasonable argument that counsel satisfied [Washington's] deferential standard.”[6] A. Howard first seeks a COA for the issue of whether his lawyer failed to investigate, develop, and present mitigating evidence of Howard’s life history and mental issues. “[T]he record is replete,” he says, “with a picture of a bumbling attorney who was doing the bare minimum to get through a trial that could not end soon enough[.]” “ Had counsel’s performance not been deficient, there is a reasonable probability that Mr. Howard would have been sentenced to life instead of death.” More concretely, Howard urges that an effective attorney would have (1) hired an expert to examine Howard and gather a life history “for mitigation purposes”;[7] (2) discovered records suggesting that Howard injured his head in 1997;[8] and (3) presented more witnesses and questioned them better. The district court rejected Howard’s theories, opining that the state courts had reasonably adjudicated them.[9] The court noted that “Howard’s trial counsel did investigate and provide witnesses and records as to Howard’s child-hood background, educational struggles, depression, and mental health issues.” The lawyer had called many “lay witnesses, consisting of close family members, extended family, educators, coaches, neighbors, and friends to testify regarding his mental decline and odd behavior throughout the years.” “[C]ounsel also [used] a trial investigator and obtained Howard’s medical and school records.” Indeed, counsel started and finished the proceedings by highlighting Howard’s mental issues. In his first remarks during guilt-phase opening arguments, the lawyer emphasized Howard’s impairments. And in closing arguments at the punishment phase, the lawyer stressed that the jury should consider Howard’s mental illness and give him life. Howard’s lawyer looped experts in, too, as the district court noted. Indeed, counsel hired a psychiatrist—Dr. Fred Fason—to conduct an examination. And twice counsel successfully moved the trial judge to appoint doctors to evaluate Howard’s competency to stand trial.[10] Naturally, those examinations unearthed evidence about Howard’s mental health. One of the evaluating psychologists—Dr. James Duncan—testified at the guilt phase [11] that Howard was impaired and possibly schizophrenic. And Dr. Fason testified at punishment about Howard’s mental shortcomings, including that he may have been schizophrenic. Howard’s case is plainly distinguishable, the district court concluded, from those in which a lawyer totally fails to examine mental health and life history. See Williams, 529 U.S. at 395–97; Lockett, 230 F.3d at 714. Howard’s lawyer pursued and presented many witnesses and experts who spoke about Howard’s mental issues and history, so, the court opined, there is undeniably a reasonable argument that the lawyer satisfied Washington‘s deferential standard.[12] To say otherwise only second-guesses the lawyer’s performance as a matter of degree. Howard’s protests of inadequate research fail to show a debatable issue when they are stacked against the lawyer’s investigative efforts and the bountiful testimony concerning Howard’s mental health.[13] “[C]umulative testimony generally cannot be the basis of an [IAC] claim.” Richards v. Quarterman, 566 F.3d 553, 568 (5th Cir. 2009). The suggestion that counsel should have gone even further—say, by finding evidence of a head injury[14] or by hiring yet another expert—does not show that the district court’s conclusion was debata-ble.[15] Indeed, Howard’s own state application admitted that his “trial lawyer did a fairly good job of presenting some type of mental deficiency.” B. Howard’s remaining arguments either do not show a debatable issue or are forfeited. 1. Howard asks leave to appeal the claim that his lawyer “failed to seek timely and relevant evaluations of the mental condition of Mr. Howard regarding his competence to stand trial.” After two trials on the matter, a jury found Howard competent. The district court decided that the state courts had reasonably held that Howard’s lawyer adequately pursued the competency issue. Howard points to several alleged omissions: His lawyer (1) “did not even consider competence until Dr. Fason urged him”; (2) failed to request an ex-pert’s review of competency until Fason suggested; (3) “did not discuss” Dun-can’s report with Duncan “until the day [the lawyer] began opening his case on guilt”; and (4) failed to request a trial on competency but, instead, waited for the state to do so. Howard did not, however, press those omissions in his federal petition or contend that they proved ineffectiveness. Instead, as the district court recognized, the petition was “silent regarding how the state habeas court [wa]s unreasonable pertaining to its findings of fact and conclusions of law” and failed to explain how the lawyer’s efforts as to competency were lackluster. We cannot grant a COA on an argument the district court had no chance to address. See Thompson, 916 F.3d at 460. Howard’s other tack is to renew his general investigation-of-mental-health contentions. Those were presented to the district court, but for reasons described, they do not raise a debatable issue or deserve to proceed. 2. Howard demands a COA on whether his lawyer failed to scrutinize the knowingness and intelligence of his Miranda waiver and eventual confession. Howard’s theory is that, if his lawyer had adequately explored his mental health, then the lawyer would have successfully contended that Howard lacked the capacity to waive his Miranda rights and confess. Howard does not suggest that he would have been acquitted were the confession excluded. Instead, he complains that the prosecutors were able to use his Mirandized statement “to demonstrate that Mr. Howard was calculating and had no remorse, something that was highlighted time and again . . . in seeking a death penalty.” Howard does not explain how a better investigation of his mental health could somehow have led to a successful challenge to his confession. He fails to engage with the district court’s reasoning that the evidence showed that Howard understood his rights and was not coerced into waiving them and confessing. Indeed, he offers no theory as to why the court’s conclusion was debatable. Regardless, for reasons described, reasonable jurists could not debate that the state courts reasonably applied federal law in determining that counsel’s investigation was good enough. 3. Howard directly appeals the denial of an evidentiary hearing. See Norman v. Stephens, 817 F.3d 226, 234 (5th Cir. 2016) (construing the same as a direct appeal). “Because [Howard's] constitutional claims fail, we need not address the merits of his evidentiary hearing claim.” Jackson v. Davis, 795 F. App’x 939, 940 (5th Cir. 2020) (per curiam) (citing Norman, 817 F.3d at 234). But even if we do, see Norman, 817 F.3d at 234 (addressing the merits despite no need), there is no abuse of discretion, see, e.g., Segundo v. Davis, 831 F.3d 345, 351 (5th Cir. 2016). * * * * * The motion for a COA is DENIED. The order denying an evidentiary hearing is AFFIRMED.
