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KING, Circuit Judge: Petitioner-Appellant Sherman Lamont Fields was convicted of murder in a- jury trial in federal district court and sentenced to death. We affirmed his conviction and sentence on direct appeal. Fields unsuccessfully sought habeas relief in the district court on numerous grounds, and now seeks a certificate of appealability to challenge the district court’s denial of habeas relief. We hold that reasonable jurists could not debate the district court’s conclusions and accordingly DENY Fields’s request for a certificate of appealability. I. FACTUAL AND PROCEDURAL BACKGROUND A. Escape and Murder of Suncerey Coleman Sherman Lamont Fields was arrested in September 2001 for being a felon in possession of a firearm, and he was held in federal custody in a detention center in Waco, Texas. In November 2001, while Fields was in custody, he bribed a correctional officer, offering him $5,000 for a key to the detention center’s fire escape. He used the key to escape on November 6. That evening, Fields met with a friend, Edward Outley, who provided Fields with a car and a handgun. Fields then visited his ex-girlfriend, Suncerey Coleman, at Hillcrest Hospital in Waco, where she was caring for her newborn child. Fields was angry at Coleman for having seen other men while he was incarcerated. Fields convinced Coleman to leave the hospital with him that evening, and drove her to Downsville, Texas, outside Waco. Fields and Coleman had sexual intercourse, and then he killed her by shooting her twice in the head. Fields hid Coleman’s body in underbrush near the road. Coleman’s body was found two weeks later, on November 21. Using a handgun, Fields later carjacked an employee of Hillcrest Hospital, Tammy Edwards, while she was exiting her car. Edwards managed to escape, and Fields drove away in her car. Police arrested Fields on November 24, 2001. In May 2003, the government charged Fields by a seven-count indictment with (1) conspiring to escape from federal custody, (2) escaping from federal custody, (3) using and carrying a firearm during and in relation to escape, resulting in intentional murder, (4) carjacking, (5) using and carrying a firearm during and in relation to carjacking, (6) felon in possession of a firearm, [and] (7) using and carrying a Ruger .22 caliber firearm during and in relation to escape. Fields, 483 F.3d at 324. The government sought the death penalty on the murder charge. B. Fields’s Trial 1. Guilt/Innocence Phase Fields’s trial took place in January and February of 2004. Fields represented himself pro se, with his appointed counsel acting as standby counsel. Fields pleaded not guilty to each charge. His defense was that he did not kill Coleman, but that his second girlfriend, Shalaykea Scroggins, did so with Outley. He contended that Scrog-gins was in “a passionately jealous rage” and shot Coleman in the back of the head, and that Outley, who was Scroggins’s sister’s boyfriend, shot Coleman a second time. The jury rejected Fields’s defense and found him guilty on all counts. 2. Punishment Phase Fields agreed to be represented by his appointed counsel during the punishment phase of the trial. After hearing the evidence, the jury recommended the death penalty. The district court sentenced Fields to death. The district court also sentenced Fields to 715 months of imprisonment on the noncapital counts. C. Post-Conviction Proceedings 1. Direct Appeal On direct appeal, we rejected Fields’s claims of sentencing error and trial error, and affirmed his convictions and sentences. Fields, 483 F.3d at 323. 2. Federal Habeas Petition Fields filed several motions seeking to vacate his conviction pursuant to 28 U.S.C. § 2255, alleging a total of forty-nine claims. The district court denied relief on all claims in its September 25, 2012 order, and found, sua sponte, that a certificate of appealability (“COA”) should not issue. Fields filed a motion to vacate or amend the district court’s order denying his § 2255 motion, among other post-judgment motions, all of which the district court denied. II. STANDARD OF REVIEW “This court may not consider an appeal from the denial of a 28 U.S.C. § 2255 motion for relief unless either the district court or this court issues a COA.” United States v. Hall, 455 F.3d 508, 513 (5th Cir .2006) (citing 28 U.S.C. § 2253(c)(1)(B)); see also United States v. Bourgeois, 537 Fed.Appx. 604, 610-11 (5th Cir.2013) (unpublished). To obtain a COA, Fields must make “a substantial showing of the denial of a constitutional right.” 28 U.S.C. § 2253(c)(2). “A petitioner satisfies this standard by demonstrating that jurists of reason could disagree with the district court’s resolution of his constitutional claims or that jurists could conclude the issues presented are adequate to deserve encouragement to proceed further.” Miller-El v. Cockrell, 537 U.S. 322, 327, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003) (citing Slack v. McDaniel, 529 U.S. 473, 484, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000)). The Supreme Court has explained that “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.” Id. at 338, 123 S.Ct. 1029. In determining whether to grant a COA, “the court of appeals should limit its examination to a threshold inquiry into the underlying merit of [the petitioner’s] claims.” Id. at 327, 123 S.Ct. 1029. This inquiry consists of “an overview of the claims in the habeas petition and a general assessment of their merits.” Id. at 336, 123 S.Ct. 1029. “[I]n a death penalty case any doubts as to whether a COA should issue must be resolved in the petitioner’s favor.” Ramirez v. Dretke, 398 F.3d 691, 694 (5th Cir.2005) (alterations and internal quotation marks omitted). III. DISCUSSION Fields seeks a COA on the following claims: that (1) he received ineffective assistance of counsel because of his trial counsels’ failure to: conduct a competent penalty phase investigation, conduct an adequate investigation related to the charged crime, and challenge expert testimony about Fields’s future dangerousness; (2) he was incompetent to waive counsel; (3) his practice cross-examination of a government witness violated his constitutional rights; (4) the government violated its Brady obligations by failing to disclose exculpatory evidence and correct false testimony at trial; (5) Fields is actually innocent; (6) the district court’s Allen charge was coercive; (7) security procedures during the trial, including the district court’s requirement that Fields wear a stun belt, were prejudicial; (8) cumulative error requires that his convictions be set aside; and (9) the district court erred by failing to grant discovery or hold an evidentiary hearing. We address each claim in turn. A. Ineffective Assistance of Counsel Fields raises several separate claims of ineffective assistance of counsel (“IAC”). His three principal contentions are that he received ineffective assistance because of trial counsels’ failure to: conduct a competent penalty phase investigation, conduct an adequate investigation related to the charged crime, and challenge expert testimony about Fields’s future dangerousness. For the reasons that follow, we deny a COA as to each of Fields’s IAC claims. 1. Penalty Phase Investigation In his § 2255 petition, Fields asserted that he received ineffective assistance of counsel because his counsel failed to conduct a competent penalty phase investigation. He included with his petition “critical mitigation evidence” that was readily available to his counsel, but which he claimed his counsel never presented to the jury. The district court reviewed this evidence and rejected Fields’s IAC claim, finding the evidence contained in his § 2255 petition duplicative of that adduced at trial. Fields now devotes nearly seventy pages of briefing to this issue, contending that reasonable jurists would debate the district court’s rejection of his IAC claim because he has established that his counsels’ performance was deficient and prejudiced him. Specifically, he contends that: (1) the district court “applied the wrong legal standard in evaluating his IAC claim”; (2) “trial counsel performed a substandard investigation and therefore presented inadequate mitigation evidence at trial”; (3) his “§ 2255 Motion presented voluminous mitigation evidence further demonstrating the ineffectiveness of counsels’] investigation”; and (4) “this new evidence establishes the prejudice caused by trial counsels’] incompetence and the reasonable probability of a different outcome had counsel been effective.” Fields’s arguments center on the specific mitigation evidence that he claims his trial counsel should have uncovered and presented during the penalty phase of the trial. This includes evidence of the terrible poverty, neglect, abuse, and trauma that he faced while growing up, his potential brain damage, his history of incarceration, and his mental illness and family history of mental illness. We have reviewed the evidence provided by Fields, and for the reasons that follow, we conclude that reasonable jurists would not debate the district court’s holding. Accordingly, we deny Fields’s claim for a COA. To succeed on an IAC claim, a defendant must show that (1) his “counsel’s representation ‘fell below an objective standard of reasonableness,’ ” and (2) the “counsel’s deficient performance prejudiced the defendant.” Roe v. Flores-Ortega, 528 U.S. 470, 476-77, 120 S.Ct. 1029, 145 L.Ed.2d 985 (2000) (quoting Strickland, 466 U.S. at 688, 694, 104 S.Ct. 2052). “[A] court must indulge a strong presumption that counsel’s conduct falls within the wide range of reasonable professional assistance.” Strickland, 466 U.S. at 689, 104 S.Ct. 2052. The objective standard of reasonableness is measured “ ‘under prevailing professional norms.’” Rompilla v. Beard, 545 U.S. 374, 380, 125 S.Ct. 2456, 162 L.Ed.2d 360 (2005) (quoting Strickland, 466 U.S. at 688, 104 S.Ct. 2052). The Supreme Court has long referred to the American Bar Association’s standards for capital defense work as “guides to determining what is reasonable.” Wiggins v. Smith, 539 U.S. 510, 524, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003); see also Bobby v. Van Hook, 558 U.S. 4, 7-8, 130 S.Ct. 13, 175 L.Ed.2d 255 (2009). “In assessing the reasonableness of an attorney’s investigation ... a court must consider not only the quantum of evidence already known to counsel, but also whether the known evidence would lead a reasonable attorney to investigate further.” Id. at 527, 123 S.Ct. 2527. The Court has explained that “ ‘[strategic choices made after thorough investigation of law and facts relevant to plausible options are virtually unchallengeable; and strategic choices made after less than complete investigation are reasonable precisely to the extent that reasonable professional judgments support the limitations on investigation.’ ” Id. (quoting Strickland, 466 U.S. at 690-91, 104 S.Ct. 2052). The Court subsequently explained that “[a] tactical decision is a precursor to concluding that counsel has developed a reasonable mitigation theory in a particular case.” Sears v. Upton, 561 U.S. 945, 130 S.Ct. 3259, 3265, 177 L.Ed.2d 1025 (2010) (per curiam) (internal quotation marks omitted). “ ‘[A] defendant who alleges a failure to investigate on the part of his counsel must allege with specificity what the investigation would have revealed and how it would have altered the outcome of the trial.’ ” Trottie v. Stephens, 720 F.3d 231, 243 (5th Cir.2013) (quoting Druery v. Thaler, 647 F.3d 535, 541 (5th Cir.2011)). Prejudice is established if “there is a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different.” Rompilla, 545 U.S. at 390, 125 S.Ct. 2456 (internal quotation marks omitted). “A reasonable probability is a probability sufficient to undermine confidence in the outcome.” Wiggins, 539 U.S. at 534, 123 S.Ct. 2527 (internal quotation marks omitted). “To assess that probability, we consider ‘the totality of the available mitigation evidence — both that adduced at trial, and the evidence adduced in the habeas proceeding’ — and ‘reweigfh] it against the evidence in aggravation.’ ” Porter v. McCollum, 558 U.S. 30, 41, 130 S.Ct. 447, 175 L.Ed.2d 398 (2009) (quoting Williams v. Taylor, 529 U.S. 362, 397-98, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000)) (alteration in original). a. Evidence of Fields’s poverty, neglect, abuse, trauma, and history of incarceration, as well as social history records and interviews of additional family members We conclude that the district court’s denial of relief on Fields’s IAC claim concerning these areas of mitigation evidence is not debatable by reasonable jurists. Because it is important to consider the mitigating evidence presented during the trial’s penalty phase before turning to the evidence in Fields’s § 2255 motion, we first review this material. Fields’s penalty-phase investigation team included his counsel (Scott Peterson and Robert Swanton), a mitigation specialist (Jane McHan, now Bye), an investigator (Dan Youngblood), and a psychiatrist (Dr. J. Randall Price). In his affidavit, Swanton explains that he asked Dr. Price “to assess Mr. Fields’[s] intelligence and to offer defense strategy opinions regarding Mr. Fields after his interviews with Mr. Fields.” He “also asked Dr. Price to assess the relationship between Mr. Fields’[s] intelligence and his ability to adapt to prison, if Fields were sentenced to life.” Swanton did not ask Dr. Price to conduct any neuropsychological testing of Fields, but he “knew Dr. Price had experience in the field of neuropsychology and would have relied on his opinion if he felt any such testing was warranted after his interviews with Mr. Fields.” In the defense’s opening statement, Peterson told the jury that Fields had a “very disruptive, a very violent childhood,” in which Fields “learned from the streets” and was exposed to his alcoholic mother’s boyfriend, who beat his mother and whipped Fields and his siblings with a belt “on a regular basis.” Peterson talked about Fields’s family’s move to the housing projects in Waco, and Fields’s exposure there to “the drugs, the violence, the weapons, the alcoholism,” and “[everything that we think of as bad in our society.” He noted several “traumatic events” in Fields’s early life, including his attempted suicide with his best friend at age fourteen, during which his friend died; the murder of another friend; his mother getting shot by her boyfriend; and his grandfather getting “run over by a drunk driver ... in Sherman’s presence.” Peterson noted that Fields had been imprisoned for an extended period, including as a teenager. Defense counsel called nine witnesses during the penalty phase of the trial. Three correctional officers testified about Fields’s recent good behavior. Jane Bye testified about Fields’s background, including the fact that his mother was on welfare around the time Fields was born; his abuse by his mother’s boyfriend, William Bradford; the fact that his mother shot Bradford, for which she was incarcerated for fifty days; the fact that Fields began committing crimes the year after his mother was incarcerated; his family’s difficult move to the projects; Fields’s exposure to drugs, guns, and other types of crimes in the projects; the lack of supervision of Fields or his siblings; Fields’s suicide attempt and his friend’s death; the fact that three of his friends died in violent fashion in 1989; the fact that Fields witnessed a drunk driver kill his grandfather; Fields’s multiple attempts to commit suicide while at the Texas Youth Commission; and the fact that Melvin Swinnie, with whom Fields’s mother was romantically involved after Bradford, shot her in the head in 1993. Next, Fields’s uncle, Vincent Green, testified about Fields’s background, including the fact that Fields was present when his grandfather was killed; that the projects were dangerous; and that Fields told Green he wanted to leave the projects after his family moved there. Fields’s grandfather’s stepson, Reverend Edward Green, also testified about Fields’s background, including the details of the day that Fields’s grandfather was killed; the fact that the projects were a rough neighborhood and not a good environment for raising children; and his opinion that Fields’s move to the projects was a “traumatic change.” Adrian Dow, a prior girlfriend, testified that Fields was a positive influence on their daughter and treated Dow with respect. Fields’s mother, Alice Swinnie, testified about Fields’s background, including that her former boyfriend, Bradford, had an alcohol problem and beat her and her children; that the abuse continued from when Fields was around two years old until he was ten or eleven; that there were violence and drugs in the projects, to which Fields was exposed; that Swinnie was absent for extended periods of time because of the multiple jobs she worked, leaving Fields and his siblings unsupervised; that she shot Bradford and spent fifty days in prison as a result; that it was especially hard on Fields when she was imprisoned; and that another man she dated shot her in the head. She also testified that she believed Fields could change his life, and do “some good things,” including continuing his education, if he received a life sentence. Lastly, Dr. Price testified about Fields’s IQ and ability to adapt to a prison environment. As this review makes clear, Fields’s counsel investigated and presented evidence of Fields’s poverty, neglect, abuse, attempted suicides, exposure to violence, incarceration while a teenager and later, and the death of close family members and friends. Thus, while Fields contends that his trial counsel should have found and presented precisely this type of evidence, the record reflects that his trial counsel did so. The mitigating evidence presented generally falls into the category of “family and social history,” as described by the ABA Guidelines: a category that includes physical and emotional abuse, domestic violence, poverty, familial instability, neighborhood environment, peer influence, and “other traumatic events such as exposure to criminal violence [or] the loss of a loved one.” ABA Guidelines. As earlier noted, the ABA Guidelines are “guides to determining what is reasonable.” Wiggins, 539 U.S. at 524, 128 S.Ct. 2527. The fact that Fields’s trial counsel investigated and presented evidence of each of these “family and social history” sub-categories is a strong indication that the district court’s conclusion, that counsels’ performance was reasonable, is not debatable. Fields’s argument that the mitigating evidence his trial counsel presented was inadequate because it was in “outline form” and “devoid of detail” is unpersuasive. The fact that the jury unanimously found the presence of nine mitigating factors, and found by a majority the presence of four other mitigating factors, belies Fields’s argument. The jury’s answers to the mitigation questions indicate that the jury credited Fields’s witnesses and gave careful consideration to the challenges that Fields faced. Nonetheless, the jury concluded that the aggravating factors outweighed the mitigating factors. Fields analogizes to Wiggins, in which the Court found counsels’ performance deficient where counsel “abandoned their investigation of [the] petitioner’s background after having acquired only rudimentary knowledge of his history from a narrow set of sources.” 539 U.S. at 524, 123 S.Ct. 2527. Fields explains that Wiggins “makes it clear that conducting some mitigation investigation does not suffice,” as opposed to conducting a full investigation. Wiggins is distinguishable and does not support Fields’s argument. In Wiggins, “counsel introduced no evidence of Wiggins’ life history” during the punishment phase of the trial. Id. at 515, 123 S.Ct. 2527 (emphasis added). The Court’s focus was on “whether the investigation supporting counsel’s decision not to introduce mitigating evidence of Wiggins’ background was itself reasonable.” Id. at 523, 123 5.Ct. 2527. The Court concluded it was not. Id. at 533, 123 S.Ct. 2527. Counsels’ investigation relied on only three sources: a psychologist’s examination, a presen-tence investigation report, and records kept by the Baltimore City Department of Social Services (“DSS”) documenting the petitioner’s placement in foster care. Id. at 523, 123 S.Ct. 2527. Counsel did not prepare any social history report, id. at 524, 123 S.Ct. 2527, and did not pursue leads suggested by the DSS documents, including the petitioner’s mother’s alcoholism or the effect of foster care on the petitioner, id. at 525, 123 S.Ct. 2527. Counsel did not discover the petitioner’s exposure to severe physical and sexual abuse by his mother and while under the care of foster parents. Id. at 516, 525, 535, 123 S.Ct. 2527. The Court concluded that counsels’ deficient performance prejudiced the petitioner. Id. at 535-36, 123 S.Ct. 2527. Here, by contrast, counsel investigated and introduced evidence of Fields’s social history through multiple witnesses, a mitigation specialist among them. Fields’s counsel investigated numerous sources, unlike the three sources relied on by trial counsel in Wiggins. Id. at 533, 123 S.Ct. 2527. As indicated by Bye’s testimony, Fields’s trial counsel and mitigation team conducted a thorough investigation of Fields’s background and social history, which revealed Fields’s physical abuse; suicide attempts; exposure to drugs, guns, and violence; and the deaths of friends and family members in violent fashion, among other topics. Finally, unlike in Wiggins, where trial counsel did not uncover pervasive sexual abuse, id. at 525, 123 S.Ct. 2527, there is no indication here that trial counsel failed to uncover or investigate any such issue in Fields’s background (with the exception of Fields’s mental health, which we address below). Lastly, Fields contends that the new evidence he offers is “materially different” from the evidence presented by trial counsel. However, our review of the evidence presented at trial, when compared to the additional evidence Fields claims his counsel should have discovered, convinces us that reasonable jurists would not disagree with the district court’s determination that the new evidence is not materially different from that presented at trial. Rather, it offers more detail about each category of mitigation evidence, but duplicates the evidence already presented. Accordingly, we conclude that reasonable jurists would not debate the district court’s holding. b. Mental illness and family history of mental illness We similarly conclude that reasonable jurists would not debate the district court’s rejection of Fields’s IAC claim with respect to his counsels’ performance in presenting mitigating evidence of Fields’s mental illness and family history of mental illness. The mental illness evidence adduced during the penalty phase of the trial consisted of the following: • Fields received psychiatric and psychological treatment while at the Texas Youth Commission (testimony of Jane Bye); • Fields’s mother suffered from mental retardation (testimony of Jane Bye); • Fields had been diagnosed with an antisocial adolescent behavior disorder (testimony of Dr. Price on cross-examination). In Fields’s habeas motion, he presented evidence of diagnoses of bipolar disorder and post-traumatic stress disorder (“PTSD”), and a family history of mental illness. In ruling on Fields’s motion, the district court acknowledged the “relative paucity of evidence regarding [Fields’s] history of mental illness and his family’s history of mental illness” that was presented during the trial, as well as the fact that “further information regarding any mental illness suffered by [Fields] or the genetic predisposition to mental illness based on his family history could have been mitigating if true.” With respect to the other categories of mitigation evidence discussed above, such as abuse and trauma, trial counsel presented some evidence of the issue, and Fields seeks to have more evidence considered now. With respect to the mental health evidence, however, trial counsel presented no evidence of Fields’s bipolar disorder or PTSD, nor of Fields’s family history of mental illness (beyond the mention of Fields’s mother’s mental retardation, which the testimony suggested may derive, in part, from her being shot in the head). Assuming without deciding that counsels’ performance was deficient, we conclude that the district court’s holding that counsels’ performance did not prejudice Fields is not debatable. The district court held that Fields could not establish prejudice because “additional evidence of [Fields’s] specific mental illnesses could possibly have been utilized as evidence that [Fields] was a future danger to society,” and the “record reflects that the government had presented compelling aggravating evidence regarding [Fields’s] future dangerousness.” We have considered “the totality of the available mitigation evidence,” and performed the required reweighing of this evidence against that in aggravation. Porter, 558 U.S. at 41, 130 S.Ct. 447: The district court’s holding is not debatable because there is not a probability “sufficient to undermine confidence in the outcome,” Wiggins, 539 U.S. at 534, 123 S.Ct. 2527, that, if trial counsel had presented the mitigating evidence of mental illness to the jury, the jury would have reached a different result. Evidence of mental illness can be mitigating, in that it can influence a jury’s appraisal of a defendant’s moral culpability. Porter, 558 U.S. at 45, 130 S.Ct. 447. However, such evidence can also be “double-edged,” as the district court noted, since it can lead a jury to conclude that a defendant poses a future risk of violence. Martinez v. Quarterman, 481 F.3d 249, 255 (5th Cir.2007); see also Vasquez v. Thaler, 389 Fed.Appx. 419, 429 (5th Cir.2010); Woods v. Thaler, 399 Fed.Appx. 884, 895 (5th Cir.2010). The mental health evidence that Fields asserts should have been presented may have led the jury to find an additional mitigating factor related to that evidence. However, even if the jury made such a finding, the jury would have weighed it, along with the other mitigating factors, against the severe aggravating factors that led the jury to impose the death penalty in the first place. Reasonable jurists would not disagree with the district court’s conclusion that the jury’s calculus would not have changed if such evidence had been presented. The jury heard ample mitigating evidence, and found nine statutory mitigating factors unanimously and another four by a majority. Nonetheless, the jury concluded that the aggravating factors outweighed these mitigating factors, and sentenced Fields to death. The jury heard testimony that Fields: escaped from prison, subsequently murdered Coleman, and later carjacked Edwards while using a gun; shot a man in the head during a drive-by shooting in 1991, pled guilty to attempted murder, and received an eight-year prison sentence for the crime; participated in another drive-by shooting in 2000; raped and beat his ex-wife, April Fields, threatened to kill her, and at one point drove her to a dark, wooded area where he made her get out of the car and pulled a gun on her, but decided not to kill her; attempted to escape from prison after his arrest for Coleman’s murder by removing an air vent in the ceiling; and engaged in violent conduct and threatened the lives of correctional officers and their families while he was imprisoned. The jury found, unanimously, that Fields “participated in attempted murders and other serious acts of violence” before killing Coleman. The jury concluded, also unanimously, that Fields “is likely to commit serious acts of violence in the future which would be a continuing and serious threat to the lives and safety of others.” Given Fields’s violent crimes, his history of violence, the jury’s finding that he posed a risk of future violence, and the fact that evidence of mental illness can be “double-edged,” see Vasquez, 389 Fed.Appx. at 429, Woods, 399 Fed.Appx. at 897, reasonable jurists would not debate the district court’s holding that the verdict would not have changed even had the jury heard evidence of Fields’s mental illnesses. Accordingly, we deny a COA. c. Potential brain damage Lastly, we conclude that reasonable jurists would not debate the district court’s rejection of Fields’s I AC claim with respect to his counsels’ performance in not further investigating or presenting mitigating evidence of brain damage. Dr. Price, the clinical and forensic psychologist and neuropsychologist who was a member of Fields’s penalty phase investigation team, stated in his declaration that he “did not conduct any neuropsychological testing on Mr. Fields as [he] did not find any suggestion of congenital or acquired brain damage.” Fields’s counsel, Swanton, stated in his declaration that he “would have relied on [Dr. Price’s] opinion if he felt any [neuropsychological] testing was warranted after his interviews with Mr. Fields.” In his habeas materials, Fields does not provide any evidence of brain damage; rather, he speculates that brain damage may have occurred due to his upbringing and attempted suicides. Based on counsels’ reliance on Dr. Price’s opinion and the lack of evidence of brain damage offered by Fields, jurists of reason would not debate the district court’s conclusion that counsels’ performance was not unreasonable. 2. Investigation of the Homicide Fields’s second IAC claim is that his counsel failed to conduct an adequate investigation into the facts of the charged homicide. Specifically, he asserted in his § 2255 petition that counsel did not interview the following three potential witnesses: Renee “Na-Na” Alberta Hampton, who Fields contends was an eyewitness to the crime.... Edward Outley III, who Fields asserted was an accomplice to the actual killer, Shalaykea Scroggins.... [And] Debra Alexander, a witness that the Government identified as one who could corroborate Fields’[s] defense that Scroggins was the actual killer. He also argued that counsel only investigated and interviewed a small number of the government’s witnesses. The district court rejected Fields’s claim, finding that he failed to indicate what facts the uncalled witnesses would have testified to or how their testimony would have changed the outcome of the trial. The district court also concluded that Fields failed to establish how additional investigation or interviews would have uncovered favorable testimony for him or otherwise altered the trial’s outcome. Fields suggests that the district court’s holding is debatable because: his counsel was ineffective; Moore v. Quarterman, 584 F.3d 454 (5th Cir.2008), indicates that he should have an opportunity to develop the factual record; the district court improperly stated that Fields never sought a continuance to subpoena witnesses, when in fact the court had foreclosed this possibility; and the district court failed to address his claim concerning his counsels’ investigation of witnesses on the government’s witness list. We deny a COA because jurists of reason could not disagree with the district court’s rejection of Fields’s arguments. “[A] defendant who alleges a failure to investigate on the part of his counsel must allege with specificity what the investigation would have revealed and how it would have altered the outcome of the trial.” Trottie, 720 F.3d at 243 (internal quotation marks omitted). We have explained that “[c]omplaints of uncalled witnesses are not favored in federal habeas corpus review because allegations of what a witness would have testified are largely speeula-five.” Sayre v. Anderson, 238 F.3d 631, 635-36 (5th Cir.2001) (internal quotation marks omitted). To prevail on such a claim, “the petitioner must name the witness, demonstrate that the witness was available to testify and would have done so, set out the content of the witness’s proposed testimony, and show that the testimony would have been favorable to a particular defense.” Day v. Quarterman, 566 F.3d 527, 538 (5th Cir.2009). Reasonable jurists would not debate the district court’s holding because Fields’s allegations about the testimony of uncalled witnesses are “largely speculative,” see Sayre, 238 F.3d at 635-36, and he fails to “allege with specificity” what the investigation would have revealed about Hampton, Alexander, and Outley, or “how it would have altered the outcome of the trial,” Trottie, 720 F.3d at 243 (internal quotation marks omitted). Fields’s counsel attempted to interview Hampton, but she refused to speak with the defense investigator, as Fields acknowledges in his petition. Moreover, Fields does not allege with specificity what Hampton would have stated had she testified; he merely asserts that she was a “potential eyewitness to the murder.” Similarly, Fields only asserts that Alexander could “corroborate] Fields’[s] defense that Scroggins was the actual killer.” Fields’s statement that Outley is “alleged to be an accomplice to the actual killer,” is also conclusory and devoid of specifics. Furthermore, Outley testified at trial, thereby providing Fields with an opportunity to cross-examine him about his alleged role in Coleman’s murder. Fields does not indicate how the testimony of any of the witnesses would have changed the outcome of the trial, Trottie, 720 F.3d at 243, and therefore, cannot establish that the district court’s holding is debatable. Moore, to which the district court analogized, does not help Fields. Like the petitioner there, Fields has not indicated what the additional witnesses “would have testified to.” Moore, 534 F.3d at 468. The fact that the petitioner in Moore received an evidentiary hearing does not entitle Fields to one, because the record is adequate to dispose of his claim, as discussed infra. Fields’s argument that his counsels’ performance was deficient because they only interviewed “four of the fifty-nine witnesses” who testified for the government is unpersuasive. As with Fields’s claims concerning Hampton, Alexander, and Outley, Fields fails to allege what the investigation of the additional government witnesses would have revealed or how it would have altered the trial’s outcome. His conclusory argument and appeal to bare numbers does not make the district court’s holding debatable. Trottie, 720 F.3d at 243. Fields’s contention that his trial counsel only investigated “73 of the 120 witnesses” on the government’s witness list, and that this investigation was limited to open-file review of the government’s work, is unconvincing for similar reasons. At no point does Fields state what his trial counsel would have discovered from additional investigation of these witnesses. Moreover, Fields does not indicate how the investigation of these other witnesses would have altered the outcome at trial. See Trottie, 720 F.3d at 243. For these reasons, we conclude that no reasonable jurist would debate the district court’s denial of Fields’s claim. 3. Failure to Adequately Challenge Expert Testimony Fields’s final standalone IAC claim is that his trial counsel failed to adequately challenge the admissibility of the testimony of Dr. Coons, the government’s expert on future dangerousness, or to adequately attack Dr. Coons’s methodology and conclusion that Fields posed a risk of future dangerousness. For the reasons that follow, we deny a COA on Fields’s claim. Because our analysis requires careful consideration of the challenges that Fields’s counsel levied against Dr. Coons at trial, we first review this material. Dr. Richard Coons, a forensic psychiatrist, testified during the penalty phase of the trial. Fields, 483 F.3d at 341. Fields’s attorneys learned what Dr. Coons would testify concerning two days before he testified. Dr. Coons did not prepare a written report. Before Dr. Coons testified, Fields’s counsel moved to examine him outside the presence of the jury to make a challenge pursuant to Daubert v. Merrell Dow Pharmaceuticals, 509 U.S. 579, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993), which the district court granted. During the voir dire, Fields’s counsel stated as a fact that “the American Psychiatric Association [“APA”] has essentially taken the position that the area of future dangerousness is not one that can be predicted with any sort of regularity or scientific regularity.” Fields’s counsel questioned Dr. Coons regarding the empirical data he relied on in reaching his determination, his awareness “of the studies that indicate that the prediction of future dangerousness is not reliable,” the lack of peer review of Dr. Coons’s findings, and the fact that Dr. Coons’s findings cannot be scientifically tested. Dr. Coons admitted that he did not perform any follow-up studies in connection with his previous determinations of future dangerousness. The court overruled Fields’s objections and allowed the government to call Dr. Coons to testify. As we explained on direct appeal, After Dr. Coons testified regarding his education and experience, the prosecutor posed a hypothetical, which consisted of the facts of the instant capital murder and some of Fields’s background and criminal history. Based upon this hypothetical, the prosecutor asked Dr. Coons whether such an individual would constitute a future danger to others, including persons in a correctional facility. Dr. Coons responded that there was a “probability of future violence.” Fields, 483 F.3d at 341. During cross-examination, Fields’s counsel elicited several admissions from Dr. Coons regarding his conclusions: Dr. Coons stated that there is a “considerable subjective element” to his opinion; he could not identify a study validating an expert’s subjective opinion about a prisoner’s future dangerousness; he admitted that his opinion had not been subjected to peer review; he admitted that he could not provide an error rate for his opinion; he admitted that he did not know the APA’s position on future dangerousness and that some members of the organization “have difficulty with the issue”; he admitted that there is a possibility Fields will not be dangerous in the future; he admitted that he had reviewed Fields’s records, and stated that he did not know of any instance of Fields “actually physically injuring a guard”; and he stated that there are studies indicating that as prisoners age, they are less likely to be violent. The district court rejected Fields’s claim, finding that he could not establish that his counsels’ performance was deficient or prejudicial. We conclude that reasonable jurists would not debate the district court’s holding, because Fields fails to show that his trial counsels’ performance was deficient, either in adequately challenging the admissibility of Dr. Coons’s testimony before trial, or in adequately attacking Dr. Coons’s methods and conclusion during trial, such as by introducing evidence to counter Dr. Coons’s assessment. Fields’s trial counsel made a Dau-bert challenge to Dr. Coons’s testimony, performed a voir dire of Dr. Coons, and objected to the admission of Dr. Coons’s testimony. See Fields, 483 F.3d at 341. Once the district court overruled counsels’ objections, counsel performed a cross-examination of Dr. Coons during which counsel elicited several admissions from him regarding his methodology and the scientific validity of his conclusions. Considering the record and these circumstances, reasonable jurists would not debate the district court’s holding that trial counsels’ performance did not fall below an objective standard of reasonableness. See Flores-Ortega, 528 U.S. at 476-77, 120 S.Ct. 1029. Fields’s counsel challenged Dr. Coons’s conclusion on multiple grounds, revealing its subjectivity and casting doubt on its scientific or statistical validity. Thus, trial counsel undertook precisely what Fields argues he failed to do: he attacked Dr. Coons’s methodology and techniques. Fields’s reliance on Gobert v. State, No. AP-76345, 2011 WL 5881601 (Tex.Crim. App. Nov. 23, 2011), and Coble v. State, 330 S.W.3d 253 (Tex.Crim.App.2010), for the proposition that these cases “fully repudiated” Dr. Coons’s methodology and techniques, and therefore demonstrate that the district court’s opinion is incorrect, is unavailing. Ineffective assistance of counsel was not an issue in Coble or Gobert with respect to Dr. Coons’s testimony. Rather, the primary question in both cases concerning Dr. Coons’s testimony was its admission pursuant to Texas’s evidentiary rules. Coble, 330 S.W.3d at 270; Gobert, 2011 WL 5881601, at *6-7. As a result, the cases’ bearing here is limited. Moreover, as earlier noted, we decided the issue of Dr. Coons’s admissibility on direct appeal, so its consideration is foreclosed here. It is true that Fields’s counsel did not call an expert to rebut Dr. Coons, as counsel did in Coble. See Coble, 330 S.W.3d at 282. However, this distinction does not indicate that the district court’s holding concerning counsels’ performance is debatable, given that counsel attacked Dr. Coons’s methodology and conclusion at length on cross-examination. Fields’s contention that his counsels’ deficient performance is evidenced by Swan-ton’s acknowledgement that he “did not conduct any additional research or review prior transcripts of Dr. Coons’[s] testimony,” and by the fact that Swanton did not prepare a written challenge to Dr. Coons’s testimony, is unpersuasive. Swanton’s affidavit indicates that while he did not conduct additional research, he did not do so because “[he] had previously tried cases involving Dr. Coons, so [he] was familiar with [Dr. Coons’s] approach to predicting future dangerousness.” Swanton notes that he “attacked Dr. Coons’fs] methodology” during his cross-examination, “rather than the ‘facts’ underlying [Dr. Coons’s] opinion.” Similarly, Swanton did not submit a written challenge to Dr. Coons’s testimony because the government did not prepare a written Dauberb report. Given our review of the record, we cannot say that reasonable jurists would debate that district court’s holding. Fields argues that his trial counsel was deficient for failing to introduce evidence that the Bureau of Prisons was equipped to prevent violence within its prisons by using super-maximum facilities. The district court rejected this argument, concluding that Fields’s counsel “reasonably focused” on establishing that Fields’s violent tendencies would decrease over time, “[r]ather than presenting evidence” on “super-secure facilities.” Jurists of reason would not debate the district court’s holding. Fields’s counsel focused on Fields’s recent improved behavior, and on studies suggesting that his behavior would continue to improve with age, rather than focusing on the safeguards available at Bureau of Prisons facilities, which “may have reinforced to the jury the idea that [Fields] would always remain a future danger,” as the district court found. Fields’s counsel called multiple prison employees who testified that Fields’s behavior had improved during his imprisonment; defense witness Dr. Price testified that he agreed with studies showing that behavioral problems decrease with age; and Dr. Coons acknowledged these studies. Moreover, Dr. Price’s affidavit explains that Swanton decided “to limit the extent of information presented about [Fields’s] risk to engage in .violent behavior in prison due to his prior behavior while incarcerated.” Fields has not shown that the district court’s holding is debatable, or given us reason to second-guess counsels’ strategic decision not to explore this topic. See Strickland, 466 U.S. at 681, 104 S.Ct. 2052. Fields also fails to establish that the district court’s holding that he was not prejudiced by any deficient performance of counsel is debatable. The jury was present for Fields’s counsels’ cross-examination of Dr. Coons, and heard the challenges to Dr. Coons’s methodology. The jury also heard other testimony that could have lead it to conclude that Fields posed a risk of future dangerousness, including testimony about his numerous prior acts of violence, successful escape from prison, escape attempt after being imprisoned for Coleman’s murder, and threats to correctional officers. Given these facts, and the jury’s unanimous findings that Fields had “participated in attempted murders” in the past and “is likely to commit serious acts of violence in the future,” reasonable jurists would not debate the holding of the district court that there is not a probability “sufficient to undermine confidence in the outcome,” Wiggins, 589 U.S. at 534, 128 S.Ct. 2527, that, if Dr. Coons’s testimony had not been admitted or counsel had offered a defense expert to rebut Dr. Coons, the jury would have reached a different result. Fields’s arguments that the admission of Dr. Coons’s testimony “worked an independent violation” of his Fifth and Eighth Amendment rights and constituted error “as a matter of federal evidence law under the Federal Death Penalty Act” are barred because we decided them on direct appeal. Fields, 483 F.3d at 343-45; see Kalish, 780 F.2d at 508. For these reasons, we conclude that reasonable jurists would not debate the district court’s holding, and We deny a COA. B. Competency to Waive Counsel Fields contends that he suffers from mental illness and was incompetent to waive counsel, that the district court’s pretrial inquiry into his competence was constitutionally inadequate, and that his counsels’ performance was deficient because counsel failed to conduct an adequate investigation into his competence “despite numerous red flags.” He contends that reasonable jurists would debate the correctness of the district court’s decision to deny relief. We conclude that reasonable jurists would not debate the district court’s holding, and deny a COA. 1. Factual Background While awaiting trial, Fields moved to appear pro se on multiple occasions, only to subsequently withdraw his motions. Again during the pretrial hearing, Fields requested to waive counsel and proceed pro se. He informed the district court that he felt his appointed counsels’ “actions are suspicious and I think they’re working with the prosecutor instead of working for me.” He stated that his counsel “prepared a strategy ... in an attempt to try to get me a life sentence when I repeatedly profess my innocence.” The district court indicated that it would not appoint replacement counsel at that point in the proceedings. The district court informed Fields of his right to represent himself, and indicated that it would need to ensure that Fields was waiving his right to counsel voluntarily and intelligently. The district court proceeded to evaluate Fields’s understanding of the nature of the proceedings and his decision to proceed pro se. The district court cautioned Fields against taking such a course of action, and twice asked Fields if he “still want[ed] to represent [him]self,” to which Fields replied in the affirmative. The government suggested that the district court arrange for an evaluation of Fields’s competency and capacity, in light of the defense’s offering of diminished capacity as a possible mitigation instruction. Fields’s defense counsel agreed, requesting that the court arrange for Fields to be examined “out of an abundance of caution.” Fields’s counsel noted that Dr. Price had evaluated Fields, and determined that he had an IQ of 114 and was “fairly bright.” The court noted that the current proceedings were taking place on a Friday afternoon, with voir dire set to begin the following Monday morning. Nonetheless, the district court arranged for an evaluation of Fields by a psychiatrist, Dr. Stephen Mark, at 8:00 a.m. that Monday morning, prior to the beginning of voir dire. Dr. Mark evaluated Fields and reported that Fields “has had some history of depression in the past and maybe some now with his current situation, but it does not interfere with the competency.” Dr. Mark stated that Fields is not psychotic. He is not organic. He appeared able to think through questions and not distract. He appeared able to make decisions adequately for himself. In terms of the specific question can he make the decision to represent himself and be competent, the answer is yes. He is competent to do so. The district court permitted Fields to proceed pro se, with his appointed counsel acting as standby counsel. 2. Applicable Law The Constitution “does not permit trial of an individual who lacks ‘mental competency.’” Indiana v. Edwards, 554 U.S. 164, 170, 128 S.Ct. 2379, 171 L.Ed.2d 345 (2008). “It has long been accepted that a person whose mental condition is such that he lacks the capacity to understand the nature and object of the proceedings against him, to consult with counsel, and to assist in preparing his defense may not be subjected to a trial.” Drope v. Missouri, 420 U.S. 162, 171, 95 S.Ct. 896, 43 L.Ed.2d 103 (1975); see also Dusky v. United States, 362 U.S. 402, 402, 80 S.Ct. 788, 4 L.Ed.2d 824 (1960) (per curiam) (“[T]he test must be whether he has sufficient present ability to consult with his lawyer with a reasonable degree of rational understanding — and whether he has a rational as well as factual understanding of the proceedings against him.”) (internal quotation marks omitted). In Faretta v. California, 422 U.S. 806, 807, 95 S.Ct. 2525, 45 L.Ed.2d 562 (1975), the Court held that the Sixth and Fourteenth Amendments include a “right to proceed without counsel when” a criminal defendant “voluntarily and intelligently elects to do so.” In Edwards, the Court addressed “the relation of the mental competence standard to the right of self-representation.” 554 U.S. at 170, 128 S.Ct. 2379. The Court clarified that “the Constitution permits States to insist upon representation by counsel for those competent enough to stand trial under Dusky but who still suffer from severe mental illness to the point where they are not competent to conduct trial proceedings by themselves.” Id. at 178, 128 S.Ct. 2379. The Court noted that “the trial judge ... will often prove best able to make more fine-tuned mental capacity decisions, tailored to the individualized circumstances of a particular defendant.” Id. at 177, 128 S.Ct. 2379. We have explained that Edwards’s “new rule applies only in the ‘exceptional’ situation where a defendant is found competent to stand trial and elects to appear pro se, but is so severely mentally ill that his self-representation threatens an improper conviction or sentence.” Panetti v. Stephens, 727 F.3d 398, 414 (5th Cir.2013), petition for cert. filed (Jan. 27, 2014) (No. 13-8453). Edwards is also “permissive, allowing the state to insist on counsel, but not requiring that the state do so.” Id. In Panetti, we concluded that Edwards is not retroactively applicable on collateral review. Id. at 414-15. There are “ ‘no fixed or immutable signs which invariably indicate the need for further inquiry to determine fitness to proceed.’ ” United States v. Flores-Martinez, 677 F.3d 699, 706 (5th Cir.2012) (quoting Drope, 420 U.S. at 180, 95 S.Ct. 896). Rather, “ ‘the question is a difficult one in which a wide range of manifestations and subtle nuances are implicated.’ ” Id. (quoting Drope, 420 U.S. at 180, 95 S.Ct. 896). “ ‘[I]n determining whether the court should order a mental competency hearing, the court must consider three factors: (1) the existence of a history of irrational behavior, (2) the defendant’s demeanor at trial, and (3) prior medical opinion on competency.’ ” Id. at 706-07 (quoting United States v. Ruston, 565 F.3d 892, 902 (5th Cir.2009)). 3. Analysis a. Fields’s competency to waive counsel The district court rejected Fields’s competency arguments, finding his waiver of counsel intelligent and voluntary, and explaining that his “demeanor before the Court at the pretrial hearing and in previous hearings reflects that he had the ability to consult with his lawyer and the Court with a reasonable degree of rational understanding and that he had a rational understanding of the criminal proceedings against him.” The district court noted that Fields’s pro se filings showed that “he rationally understood the criminal proceedings.” As a result, the court concluded that Fields was competent to waive his right to counsel. Fields argues that the district court failed to reevaluate its competency conclusion and rejected Fields’s new evidence, and that he is therefore entitled to relief on his claim. He contends that his mental illnesses and their symptoms, including “paranoid ideation, delusional thinking, irritability, impaired judgment and impulse control, and grandiosity,” impaired him to such a degree that he did not meet the Dusky standard for mental competency, rendering him unfit to “stand trial, waive counsel and proceed with his own defense.” He asserts that the evidence from his § 2255 motion supports this argument, including: a declaration from Dr. George Woods, a psychiatrist, opining that Fields’s symptoms “impaired his competency to waive his right to counsel” and that Fields was not “competent to waive counsel and/or represent himself’; documents reflecting that Fields was hospitalized at a psychiatric hospital as a teenager, during which time he was diagnosed with PTSD and evaluated as potentially having bipolar disorder; and his inmate grievance reports, submitted while he was awaiting trial, which contain complaints that his prison guards were conspiring to murder him, and “clearly evidence paranoid ideation and delusional thinking.” We conclude that jurists of reason would not disagree with the district court’s holding, because Fields does not show that his competency fell below a standard that would have required the district court to deny his request to represent himself. Dr. Woods’s declaration, executed in 2010, six years after Fields’s trial, is not sufficient to establish that the district court’s careful and reasoned decision that Fields was competent to waive counsel is debatable. We note that the district court reached its conclusion after considering Fields’s pro se oral motion for access to a law library and his motion to change venue, questioning Fields about his decision to waive counsel, speaking with Fields’s counsel about his competency, arranging for Fields’s psychiatric evaluation by Dr. Mark, and considering the results of Dr. Mark’s evaluation. Reasonable jurists would not debate the district court’s conclusion that its inquiry into the issue demonstrated that Fields “ha[d] sufficient present ability to consult with his lawyer with a reasonable degree of rational understanding,” and a “rational as well as factual understanding of the proceedings against him.” Dusky, 362 U.S. at 402, 80 S.Ct. 788. Considering all the circumstances, and acknowledging that “the trial judge ... will often prove best able to make more fine-tuned mental capacity decisions, tailored to the individualized circumstances of a particular defendant,” Edwards, 554 U.S. at 177, 128 S.Ct. 2379, we conclude that the district court’s holding is not debatable. Fields argues that his delusional belief that his attorneys were conspiring against him was not rational, and that therefore, he did not have the requisite rational understanding of the proceedings against him or the present ability to consult his attorney. This argument is unpersuasive. Reasonable jurists would not disagree with the district court’s conclusion that the factors noted above — Fields’s demeanor at trial, his pro se motions, and Dr. Mark’s evaluation — indicate that Fields was competent to waive his right to counsel. Fields’s reliance on documents from his teenage years suggesting PTSD and bipolar disease, and his inmate grievance reports, is unavailing. The documents regarding Fields’s psychiatric evaluations as a teenager date from 1989. As such, they do not call into question the district court’s conclusion about Fields’s rational understanding of the proceedings against him, or his ability to consult with his counsel, at the time of his trial twenty-five years later. Similarly, the inmate grievance reports date from April through July of 2003, approximately six months before Fields’s trial began in January 2004, and likewise would not cause reasonable jurists to disagree with the district court’s conclusion about Fields’s competency at the time of trial. Fields’s reliance on Edwards is also unavailing. The district court concluded that Edwards had no bearing, because the case provides the trial court with “discretionary authority” to consider competency under a higher standard, but does not so require. Reasonable jurists would not disagree with the district court. As we have recently explained, “in Edwards, the Supreme Court addressed the constitutionality of the denial of the right to self-representation; the Court did not address the competency of a defendant who is granted the right to self-representation, nor did it suggest that a trial court which allows a defendant to represent himself is required to first ascertain that he is capable of doing so.” United States v. West, 567 Fed.Appx. 240, 241, 2014 WL 1797725, at *1 (5th Cir. May 7, 2014); see also Panetti 727 F.3d at 414 (noting that Edwards is permissive). Thus, reasonable jurists would not debate that Edwards is not applicable here. Even assuming Edwards is relevant, Fields has not shown that his competency fell below a standard that would have required the district court to deny his request to represent himself. See id.; Edwards, 554 U.S. at 178. Based on the lack of probative evidence tending to show incompetence, we cannot say that reasonable jurists would find the district court’s decision debatable or wrong. See Wilkins v. Stephens, 560 Fed.Appx. 299, 312-13, 2014 WL 1202524, at *10 (5th Cir.2014). b. Adequacy of the district court’s pretrial inquiry Fields contends that the district court erred by relying on Fields’s counsels’ failure to contest competency “as proof of Fields’[s] competency”; relying on Dr. Mark’s evaluation, which was “wholly uninformed”; relying on Dr. Price’s evaluation of Fields’s academic potential; conducting a hearing of only one minute in duration; and failing to consider if Fields’s waiver of counsel was rational. The district court rejected Fields’s arguments, holding that Dr. Mark’s thirty-minute examination, “coupled with” Fields’s demean- or at trial, his attorneys’ observations, and Dr. Price’s evaluation focusing on his intelligence, did not deprive Fields of his constitutional rights. Fields suggests that the district court’s holding is wrong, entitling him to relief. For the reasons noted supra, reasonable jurists would not debate the district court’s holding that Fields was competent to waive his right to counsel. Similarly, reasonable jurists would not debate the district court’s determination that its pretrial inquiry into Fields’s competency was adequate. The district court considered several factors in finding Fields competent, including its interactions with him, his pro se motions, counsels’ interactions with him, and Dr. Mark’s evaluation. The district court did not rely on any single factor as “proof’ of Fields’s competency. Fields’s argument that the hearing does not satisfy due process because it lasted only one minute is unavailing. In fact, the competency hearing was spread over two days, and involved the district court consulting Fields, counsel for both sides, and Dr. Mark. Contrary to Fields’s contention, in rejecting his § 2255 petition, the district court did consider whether his waiver was rational, and concluded that Fields had the ability to consult with counsel “with