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BIRCH, Circuit Judge: John Errol Ferguson (“Ferguson”), a Florida prisoner convicted of murder and sentenced to death, filed a federal habeas corpus petition pursuant to 28 U.S.C. § 2254 in which he made at least eleven claims. He also moved to stay the federal habeas proceedings based on his alleged incompetency, a motion denied by the district court, which held an evidentiary hearing on the issue and found him competent to proceed with the petition. The court subsequently denied Ferguson’s petition in its entirety, but granted a certificate of appealability (“COA”) on all of the issues raised therein. Ferguson has appealed the district court’s dismissal of nine of his claims and also challenges that court’s denial of his motion to stay the proceedings. The State of Florida filed a cross-appeal regarding the district court’s decision to hold an evidentiary hearing on the issue of Ferguson’s competency. After thoroughly reviewing the record and the parties’ briefs and hearing oral argument, we AFFIRM the district court’s denial of Ferguson’s petition and motion to stay. I. BACKGROUND A. Factual Background Ferguson received the death penalty in two Florida state cases in which he was convicted of a total of eight counts of first-degree murder. Six of those counts stemmed from his first trial, which dealt with events that took place in Carol City, Florida in July 1977. The second trial, which involved the other two murder counts, addressed crimes occurring in Hialeah, Florida in January 1978. 1. The Carol City Murders On the evening of 27 July 1977, Ferguson, posing as a Florida Power and Light employee, received permission from Margaret Wooden to enter her home. After checking several rooms, he drew a gun, tied and blindfolded her, and let into the house two men who joined him in looking for drugs and money. About two hours later, six of Wooden’s friends, including the homeowner, Livingston Stocker, came to the house and were searched, tied, and blindfolded by Ferguson and his accomplices. Shortly thereafter, Wooden’s boyfriend, Michael Miller, entered the house and also was bound and searched. Miller and Wooden eventually were placed in the bedroom, and the six other bound friends were in the living room. At some point, a mask on one of Ferguson’s Mends fell and revealed his face. At the time, Wooden and Miller were kneeling on the floor with their upper bodies sprawled across the bed. Wooden heard shots from the living room, saw a pillow coming toward her head, and then was shot. She witnessed Miller being fatally shot as well. Wooden did not see the shooter, though she did hear Ferguson run out of the room. She managed to escape and ran to a neighbor’s house to call the police. When the police arrived, they found six dead bodies, all of whom had their hands tied behind their backs and had been shot in the back of the head. Only two of the victims, Wooden and Johnnie Hall, survived. Hall testified at Ferguson’s trial about the methodical execution of the other victims. 2. The Hialeah Murders On the evening of 8 January 1978, Brian Glenfeld and Belinda Worley, both seventeen, left a Youth-for-Christ meeting in Hialeah, Florida. They were supposed to meet friends at an ice cream parlor, but never arrived. The next morning, two passersby discovered their bodies in a nearby wooded area. Glenfeld had been killed by a bullet to the head and also had been shot in the chest and arm. Worley was found several hundred yards away under a dense growth. All of her clothes, except for her jeans, were next to her body, and she had been shot in the back of the head. An autopsy revealed that she had been raped. At trial, there was testimony that she had been wearing jewelry, but none was found with the bodies. The cash from Glenfeld’s wallet, which was found in Worley’s purse near her body, also had been removed. On 5 April 1978, police arrested Ferguson at his apartment pursuant to a warrant for unlawful flight to avoid prosecution in connection with the Carol City murders. At the time of his arrest, police found in his possession a .357 magnum, which was capable of firing .38 caliber bullets, the same kind used to kill Glenfeld and Worley. The gun was registered to Stocker, one of the victims in the Carol City murders. At some point after Ferguson’s arrest, he confessed to killing “the two kids,” i.e., Glenfeld and Worley. B. Procedural Background 1. Trials and Direct Appeals Ferguson was indicted in July 1977 for, inter alia, six counts of first-degree murder in connection with the Carol City murders, and in January 1978 for, inter alia, two counts of first-degree murder in connection with the Hialeah murders. He was not incarcerated until his arrest for the Hialeah murders. Both cases went to trial in the Circuit Court for the Eleventh Judicial Circuit of Florida and were presided over by the same judge. Ferguson was tried alone for the Carol City murders and convicted on all counts, except for one of the armed robbery counts. After an advisory sentencing hearing, the jury recommended death. The judge followed the jury’s recommendation and imposed six death sentences, along with two consecutive sentences of thirty years of imprisonment for the attempted murders of Hall and Woodson and three sentences of life imprisonment for attempted robberies of three of the victims. At the Hialeah trial, Ferguson mounted an unsuccessful insanity defense and was convicted on two counts of first-degree murder. The jury recommended the death penalty, and the judge imposed two death sentences. In separate opinions on direct appeal, the Florida Supreme Court affirmed all of the convictions in both cases but vacated and remanded the death sentences due to sentencing errors. With respect to the Carol City case, the court found that the trial judge had relied on improper aggravating factors. For the Hialeah trial, the court found that the judge had not considered statutory mitigating factors. The Florida Supreme Court noted in both cases that an additional jury sentence advisory verdict would be unnecessary on remand. A different judge heard the cases on remand because the original trial judge had left the bench in the interim. Without holding an evidentiary hearing or impaneling a jury to make recommendations, the presiding judge imposed eight death sentences for the murders in the two cases. The Florida Supreme Court affirmed those sentences in a consolidated appeal. See Ferguson v. State, 474 So.2d 208 (Fla.1985) (Ferguson III). 2. Florida Post-Conviction & Habeas Proceedings In October 1987, Ferguson and his mother, Dorothy Ferguson, acting as next friend, filed a timely motion for post-conviction relief, pursuant to Rule 3.850 of the Florida Rules of Criminal Procedure, which set forth six claims. For the purposes of this appeal, the relevant claims were an ineffective assistance of counsel (“IAC”) claim based on trial counsel’s failure to investigate and present evidence with respect to statutory mitigating factors and a Hitchcock claim based on the trial court’s jury instructions regarding mitigating factors. Shortly thereafter, Ferguson moved to stay the proceedings on the grounds that he was incompetent to participate in them or to assist counsel by answering questions. The circuit court denied this motion in February 1989. Ferguson’s counsel subsequently moved to disqualify the post-conviction judge based on ex parte contacts between the judge and the prosecutors. The circuit court denied this motion because it was untimely, was not in compliance with Florida procedural requirements, and did not provide an adequate factual foundation for the belief that the judge would be prejudiced against Ferguson. Ferguson’s counsel then filed a petition for a writ of prohibition based on ex parte contacts between the judge and the prosecutors. The Florida Supreme Court denied this petition and the United States Supreme Court denied the subsequent petition for a writ of certiorari on the issue. See Ferguson v. Snyder, 493 U.S. 945, 110 S.Ct. 353, 354, 107 L.Ed.2d 341 (1989) (mem.) (Snyder I); Ferguson v. Snyder, 548 So.2d 662 (Fla. 1989) (table) (Snyder II). In September 1989, Ferguson filed a supplement to his 3.850 petition, in which he raised ten claims, including a claim regarding racially discriminatory peremptory challenges and a Brady claim regarding improper prosecutorial withholding of evidence. In response to a motion by the State, the circuit court struck many of the claims in Ferguson’s original and supplemental petitions, including his peremptory challenge claim. The circuit court held an evidentiary hearing in May 1990 on the remaining claims and issued an order the following month denying the remainder of Ferguson’s 3.850 motion. One month later, Ferguson moved to supplement his 3.850 petition with an additional ground for relief based on the State’s failure to correct false testimony presented at the sentencing phase of the Carol City trial. The circuit court dismissed this motion as untimely. On appeal, the Florida Supreme Court affirmed the circuit court’s denial of the 3.850 motion. See Ferguson v. State, 593 So.2d 508, 513 (Fla.1992) (Ferguson IV). Ferguson also petitioned the Florida Supreme Court for a writ of habeas corpus around the same time, which the court denied. See Ferguson v. Singletary, 632 So.2d 53, 59 (Fla.1993) (Ferguson V). In his petition, he raised four claims, only one of which is relevant for this appeal — that he was resentenced without impaneling a new jury or holding an evidentiary hearing. The Florida Supreme Court found that Ferguson had failed to preserve this issue before the circuit court and thus was procedurally barred from raising it in his petition. 3. Federal Habeas Proceedings Ferguson, along with his mother as next friend, filed his first federal habeas petition, the subject of this action, in the United States District Court for the Northern District of Florida in March 1995. He concurrently moved to stay the federal habeas proceedings due to his alleged incompetence, a motion which the district court denied in March 1999. In July 1999, Ferguson filed a motion in the Florida Circuit Court seeking to reinstate several of the claims he raised in his 3.850 motion. He based his motion on Carter v. State, 706 So.2d 873 (Fla.1997) (per curiam), which required courts to hold competency hearings in post-conviction proceedings when certain circumstances are present. Ferguson asserted that this constituted a fundamental change in the law and, as a result, applied retroactively. The circuit court denied his motion, and the Florida Supreme Court affirmed. See Ferguson v. State, 789 So.2d 306, 315 (Fla.2001) {Ferguson VI). The latter found that Carter applied retroactively but concluded that the circuit court did not abuse its discretion in finding Ferguson competent to proceed with his 3.850 petition. In anticipation of filing the motion to reinstate his 3.850 claims, Ferguson asked the federal district court in July 1999 to stay the proceedings so that he could exhaust state remedies. The district court granted the stay in May 2000, which it lifted in August 2001. As part of the latter order, the court permitted Ferguson to filed an amended habeas petition to address changes in both the law and his mental state. In August 2003, the district court again granted him leave to file an amended petition to reflect changes in the law. Ferguson filed a second amended petition a month later and also moved to stay the proceedings because of his alleged incompetence. In July 2004, the district court scheduled an evidentiary hearing to determine whether Ferguson was competent to assist counsel in the habeas proceedings. A five-day hearing was held in December 2004, at which six expert witnesses testified regarding Ferguson’s mental state. On 19 May 2005, the district court issued an order finding Ferguson competent to proceed and denying the motion to stay the proceedings. That same day, the court also issued an order denying Ferguson’s second amended habeas petition. Ferguson appealed both of these decisions, and the State cross-appealed the district court’s decision to grant an evidentiary hearing. The district court granted Ferguson’s motion for a COA “in its entirety” for the reasons articulated in Miller-El v. Cockrell, 537 U.S. 322, 338, 123 S.Ct. 1029, 1040, 154 L.Ed.2d 931 (2003). R4-113. II. DISCUSSION On appeal, Ferguson asserts that the district court erred in denying nine claims in his habeas petition relating to various aspects of his trial, resentencing, and state post-conviction proceedings. He also maintains that the court, in finding him competent to proceed with his federal habeas claim and denying his motion to stay, violated his right not to proceed while incompetent. The State, in its cross-appeal, argues that the district court improperly held an evidentiary hearing to determine Ferguson’s competency. We address these issues in turn. A. Legal Standards Applicable to This Appeal Because Ferguson filed his petition in 1995, one year prior to the effective date of the Antiterrorism and Effective Death Penalty Act of 1996 (“AEDPA”), we apply pre-AEDPA law to his claim. See Lindh v. Murphy, 521 U.S. 320, 326-27, 336, 117 S. Ct. 2059, 2063, 2068, 138 L.Ed.2d 481 (1997). However, since he initiated this appeal after the effective date of AEDPA, all questions of appellate procedure are governed by post-AEDPA law. See Slack v. McDaniel, 529 U.S. 473, 481-82, 120 S.Ct. 1595, 1602-03, 146 L.Ed.2d 542 (2000). ‘When reviewing the district court’s denial of a habeas petition, we review questions of law and mixed questions of law and fact de novo, and findings of fact for clear error.” Nyland v. Moore, 216 F.3d 1264, 1266 (11th Cir.2000) (per curiam). A state court’s findings of fact are entitled to a presumption of correctness, unless one of the exceptions discussed in § 2254(d) would be applicable. See Hardwick v. Crosby, 320 F.3d 1127, 1158 (11th Cir.2003). We also do not consider issues or arguments raised for the first time on appeal. See Nyland, 216 F.3d at 1266. We “may not consider claims that have been defaulted in state court pursuant to an adequate and independent state procedural rule, unless the petitioner can show cause for the default and resulting prejudice, or a fundamental miscarriage of justice.” Zeigler v. Crosby, 345 F.3d 1300, 1304 (11th Cir.2003) (per curiam) (quotation marks and citation omitted). A claim also would be “procedurally defaulted if the petitioner fails to raise the claim in state court and it is clear from state law that any future attempts at exhaustion would be futile.” Id. (quotation marks and citation omitted). We defer to the state court’s findings regarding procedural default. See id. We review the decision to grant or deny an evidentiary hearing for abuse of discretion. See Kelley v. Secretary for the Dep’t of Corr., 377 F.3d 1317, 1333 (11th Cir.2004). For pre-AEDPA suits, we have held that a district court must hold an evidentiary hearing if: (1) the merits of the factual dispute were not resolved in the state hearing; (2) the state factual determination is not fairly supported by the record as a whole; (3) the fact-finding procedure employed by the state court was not adequate to afford a full and fair hearing; (4) there is a substantial allegation of newly discovered evidence; (5) the material facts were not adequately developed at the state-court hearing; or (6) for any reason it appears that the state trier of fact did not afford the habeas applicant a full and fair fact hearing. Id. at 1334 (quotation marks and citation omitted). B. Ineffective Assistance of Counsel During Penalty Phase Ferguson asserts that he was denied the effective assistance of counsel during the sentencing phase of both of his trials because his attorneys failed to investigate and present mitigating evidence regarding his family background and history of mental illness. He contends that his counsel failed to pursue all such evidence that reasonably could have been obtained and thus did not conduct the kind of reasonable investigation contemplated in Wiggins v. Smith, 539 U.S. 510, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003), and Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). He maintains that this failure was highly prejudicial because of the compelling nature of the undiscovered mitigating evidence. Ferguson cites a number of relevant facts of which his attorneys were not aware: that he was raised in extreme poverty and had no running water or electricity at times; that he had an alcoholic father who died when Ferguson was thirteen years old, that he had to deal with his mother’s abusive boyfriends; and that, at age twenty-one, he was shot four times and almost killed by a police officer. He also asserts that he repeatedly was diagnosed as suffering from paranoid schizophrenia, was placed in multiple mental hospitals during the late 1960s and early 1970s, was twice found not guilty by reason of insanity, and was examined by multiple doctors in the years preceding the Carol City and Hialeah murders, all of whom diagnosed him as schizophrenic, psychotic, or hallucinating. We analyze IAC claims under the two-prong test established in Strickland, which requires us first to determine whether counsel’s performance “fell below an objective standard of reasonableness” and then to decide whether this deficient representation prejudiced the petitioner’s defense. Strickland, 466 U.S. at 687, 104 S.Ct. at 2064. In assessing the first prong of the Strickland test, we apply a “strong presumption that counsel’s performance was reasonable and that counsel made all significant decisions in the exercise of reasonable professional judgment.” Williams v. Allen, 542 F.3d 1326, 1337 (11th Cir. 2008) (quotation marks and citation omitted). For an attorney’s performance to be unreasonable, it must fall “outside the wide range of professionally competent assistance.” Strickland, 466 U.S. at 690, 104 S.Ct. at 2066. We have noted that an attorney’s duty to conduct a reasonable investigation includes looking at a defendant’s background for possible mitigating evidence. See Williams, 542 F.3d at 1337. Though “[t]his duty does not necessarily require counsel to investigate every evidentiary lead,” an attorney’s “decision to limit an investigation must flow from an inform p.d judgment.” Id. (quotation marks and citation omitted). As a result, when evaluating the reasonableness of an attorney’s investigation we “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.” Wiggins, 539 U.S. at 527, 123 S.Ct. at 2538. With respect to the prejudice prong of the Strickland test, we focus on whether the petitioner has established “that there is a reasonable probability that, but for counsel’s unprofessional errors, the result in the proceeding would have been different.” Strickland, 466 U.S. at 694, 104 S.Ct. at 2068. For a probability to be “reasonable” it must be “sufficient to undermine confidence in the outcome” of the proceeding. Id. at 694, 104 S.Ct. at 2068. We must consider the totality of the evidence to determine whether the petitioner was prejudiced by counsel’s errors. See Williams, 542 F.3d at 1342. 1. The Carol City Trial Ferguson maintains that the performance of his counsel in the Carol City case, Fred Robbins, was deficient because Robbins conducted an inadequate investigation into potential mitigating evidence regarding Ferguson’s mental history and family background. According to Ferguson, Robbins’s mental health investigation consisted solely of reading four reports, written in 1978, that discussed Ferguson’s competence to stand trial. Those reports noted that Ferguson had undergone psychiatric examinations during the early 1970s; however, Robbins did not attempt to locate records from those examinations. Additionally, Robbins did not examine Ferguson’s criminal records, which would have shown that Ferguson twice had been found not guilty of various crimes for reason of insanity. Ferguson contends that Robbins’s family history investigation was equally unreasonable. Robbins spoke with Ferguson’s mother and sister but never asked them about his upbringing, and Robbins’s conversation with Ferguson’s sister addressed only Robbins’s potential retention as counsel. Robbins also apparently made no attempt to locate public records about Ferguson or to contact his siblings, even though they lived nearby. The Florida Supreme Court rejected this claim during the 3.850 proceedings. The court noted that, although Robbins had “not exhausted] all available sources of information ..., this was not a case in which the attorney conducted only minimal investigation.” Ferguson IV, 593 So.2d at 510. It found that Robbins was aware of Ferguson’s mental history and made the tactical decision not to call as witnesses those doctors who had investigated Ferguson. The court found this strategy to be reasonable since presenting such evidence could have opened the door to damaging rebuttal evidence from the State, ie., that Ferguson had sociopathic tendencies and was exaggerating his symptoms. It therefore concluded that Ferguson had not satisfied his burden of showing either deficient performance or prejudice under the Strickland test. See id. at 511-12. The district court reached the same conclusion in the federal habeas proceedings. It found that Robbins had conducted some investigation into Ferguson’s history of mental illness and, based on that investigation, made “a reasonable tactical decision ... to avoid potentially greater prejudice from damaging information that would have been introduced to the jury regarding [Ferguson’s] malingering and anti-social personality disorder.” R4-108 at 32. The court likewise found that the Robbins had conducted a “reasonable investigation into [Ferguson’s] background” and made a “reasonable tactical decision” in light of this investigation to focus on creating lingering doubt about his guilt. Id. It also determined that, even if the investigation was unreasonable, any failure in that regard would not undermine confidence in the outcome of the proceedings given the overwhelming aggravating factors involved. The court therefore concluded that Ferguson had not met the second prong of the Strickland test. Even assuming arguendo that Robbins’s performance was deficient, Ferguson has not shown prejudice resulting from that deficient performance. The resentencing judge found five aggravating circumstances in this case: (1) Ferguson previously had been convicted of “three felonies involving the use of, or threat of, violence to some person;” (2) the murders were committed while Ferguson “was engaged in the commission of multiple robberies;” (3) the murders were committed “for the purpose of avoiding or preventing a lawful arrest;” (4) the murders were “especially heinous, atrocious and cruel;” and (5) the crimes involved homicides “committed in a cold, calculated, and premeditated manner without any pretense of moral or legal justification.” App. MM, Vol. 3 at 1-6. By comparison, the only possible mitigating circumstance identified by any of the courts assessing Ferguson’s case was that there was some evidence to indicate that Ferguson might have been suffering severe mental disturbance at the time of murders and that he had an impaired capacity to appreciate the criminality of his conduct. All of these findings are entitied to a presumption of correctness, and the parties identify no basis for questioning this presumption. See Hardwick, 320 F.3d at 1158. In our view, the aggravating circumstances far outweigh any mitigating factors, even taking into account the evidence that Robbins failed to uncover. The facts of this case are extreme, including multiple execution-style killings after a prolonged period in which the victims were bound and blindfolded. We agree with the resentencing court that “[t]he entire action of [Ferguson] and his co-conspirators reflects not only an absolute lack of concern for human life or dignity but also a barbaric cruelty.” App. MM, Vol. 8 at 6. As a result, we do not believe it is reasonably probable that the evidence Ferguson cites would lead a jury to disregard such cruel circumstances and impose a different sentence. We thus find that Ferguson has not established prejudice from this ineffective assistance and therefore conclude that the district court correctly denied habeas relief with respect to this part of Ferguson’s IAC claim. 2. The Hialeah Trial Ferguson also contends that his counsel’s performance during the sentencing phase of the Hialeah trial was deficient. He asserts that Bruce Phelps, the attorney in charge of his penalty phase presentation, made no meaningful effort to investigate Ferguson’s family history. In support of this argument, Ferguson cites Phelps’s failure to discuss potential mitigating evidence with Ferguson’s siblings and to recall Ferguson’s mother as a witness during sentencing after she broke down on the witness stand before he could elicit any meaningful testimony. Ferguson also maintains that Phelps was deficient in not presenting evidence of Ferguson’s mental illness during sentencing. Ferguson concedes that Phelps put forth mental health history evidence during the guilt phase of the trial as part of an unsuccessful insanity defense. Nevertheless, Ferguson contends that Phelps had a responsibility to recall the mental health experts so they could speak directly to the statutory mitigating factors because of the inherent difference between those factors and the requirements needed to make out an insanity defense. Furthermore, Ferguson maintains that this deficiency prejudiced his case, particularly since at least two jurors voted against the death penalty, even in the absence of the missing evidence. The Florida Supreme Court rejected Ferguson’s arguments during the 3.850 proceedings, finding both that Phelps’s performance had not been deficient and that there was no resulting prejudice to Ferguson even assuming deficiency. The court noted that, although Phelps failed to present any mitigating evidence regarding Ferguson’s mental history during the penalty phase, it was reasonable to assume that there would have been no net benefit to presenting more mental health evidence since there already had been testimony about Ferguson’s mental health during the guilt phase. The court also noted that Phelps had spoken with family members and found that his failure to recall Ferguson’s mother was “reasonable in light of her emotional state.” Ferguson IV, 593 So.2d at 511. The district court in the federal habeas proceedings reached a similar conclusion. It found that Ferguson’s counsel made a “tactical decision to focus on mental health mitigators during sentencing! ] and to appeal to the jury’s sense of sympathy for [Ferguson’s] mental health condition.” R4-108 at 34. The court deemed it reasonable, in light of this trial strategy, for Ferguson’s counsel not to recall his mother or to reintroduce potentially duplicative mental health evidence during the penalty phase of the trial. In addition, the court noted that there was no reasonable probability that any juror would find that the unpresented mitigating evidence outweighed the “overwhelming aggravating factors” present in the case. Id. at 35. As in the Carol City trial, even if we assume that Ferguson’s Hialeah trial counsel was deficient during the penalty phase, it is not reasonably probable that the jury would have imposed a different sentence had they considered the missing mitigation evidence. On resentencing, the circuit court found six aggravating factors: (1) Ferguson previously had been convicted of four felonies involving the use or threat of violence; (2) the murders occurred while Ferguson was “engaged in the commission of rape and robbery;” (3) the murders were committed to avoid a lawful arrest; (4) the murders were “committed for pecuniary gain;” (5) the murders were “especially heinous, atrocious, and cruel;” and (6) Ferguson’s crimes were committed “in a cold, calculated, and premeditated manner without any pretense of moral or legal justification.” App. MM, Vol. 3 at 13-16. The only potential mitigating factor the court identified was that Ferguson might have been suffering from extreme mental disturbance and been impaired in his ability to appreciate the criminality of his conduct. We find that the aggravating factors significantly outweighed any mitigating evidence, including that which was not presented to the jury. The facts of the Hialeah murders are just as cruel and shocking as those of the Carol City killings. One of the victims, Worley, suffered extreme physical abuse, including being apparently raped, prior to being shot in the head and left partially nude by the roadside. The other victim, Glenfeld, was shot twice, both before and after Worley had been sexually assaulted, and murdered. Admittedly, at least two jurors decided not to impose the death penalty even in the face of such circumstances. Nevertheless, the missing evidence likely would not have changed the outcome. Notably, most of the evidence regarding Ferguson’s medical background already had been presented during the guilt phase of the trial, so the jury considered that evidence in sentencing him to death. The missing evidence thus primarily involved Ferguson’s family history. Although it is possible that evidence of Ferguson’s mental history might have caused some jurors to recommend a sentence rather than death, we do not find that this was reasonably probable given the wealth of aggravating circumstances. See Parker v. Secretary for the Dep’t of Corr., 331 F.3d 764, 783 & n. 16 (11th Cir.2003) (noting that the proper standard of review is “whether the jury’s failure to hear the mitigating evidence undermines the confidence in its verdict, thus demonstrating a reasonable probability of a different result” rather than whether the result “would have been different absent the deficient performance”) (alterations, quotation marks, and citation omitted). Accordingly, we find that Ferguson has not met the prejudice prong and conclude that the district court correctly denied Ferguson habeas relief with respect to his IAC claim regarding the penalty phase of the Hialeah trial. C. Hitchcock Error Ferguson contends that the judge’s instructions to the jury at both the Hialeah and Carol City trials limited the jury’s ability to consider non-statutory mitigating factors, in violation of Hitchcock. He maintains that such limitation thus denied him a fair sentencing in both cases. This claim requires us to determine first whether a Hitchcock error occurred and then whether any such error was harmless. We have noted that, “[a]lthough whether a Hitchcock error occurred is a legal question, it is almost entirely dependent upon the answer to a question of fact: did the sentencing judge consider any and all non-statutory mitigating circumstance evidence that was presented to him?” Quince v. Crosby, 360 F.3d 1259, 1266 (11th Cir.2004) (quotation marks and citation omitted). Accordingly, we have deemed statements by the Florida Supreme Court “that the sentencing judge did not limit his consideration to only statutory mitigating circumstances” to be findings of fact that, for preAEDPA cases, should be upheld if it “is fairly supported by the record.” Id. at 1267. Ferguson asserts that this standard is inapplicable here, because the issue is whether the jury, not the judge, limited its consideration to statutory mitigating factors, a question for which there would be no factual basis because the jury does not make written findings of fact. He suggests that we instead are analyzing the propriety of jury instructions, which would be a question of law subject to de novo review. See United States v. Drury, 396 F.3d 1303, 1313 (11th Cir.2005). We believe the correct approach is to treat Ferguson’s claim as raising a mixed question of law and fact. The validity of the jury instructions under Hitchcock would be a legal question. However, determining what the jury relied on in sentencing Ferguson entails a factual inquiry looking solely at the text of the instructions. Admittedly, since the jury does not have to make written findings, we cannot say for certain whether jurors actually limited their consideration to statutory mitigating factors. Nevertheless, we deem it appropriate to assume that, in sentencing Ferguson, the jury followed the court’s instructions and that, as a factual matter, the scope of its analysis would reflect how a reasonable person would view the instructions. See United States v. Siegelman, 561 F.3d 1215, 1239 (11th Cir.2009) (per curiam) (“The jury is presumed to follow the district court’s instructions.”). We therefore evaluate de novo the issue of whether a Hitchcock error occurred. See Nyland, 216 F.3d at 1266. In so doing, we must examine the totality of the circumstances in which the instructions were given. See Card v. Dugger, 911 F.2d 1494, 1522 (11th Cir.1990). Even if we find a Hitchcock error to have occurred here, we can still deny Ferguson’s claims if we determine that the error was harmless. Whether an error was harmless is a mixed question of law and fact that we review de novo. See Smith v. Singletary, 61 F.3d 815, 817 (11th Cir.1995) (per curiam). For Hitchcock errors, we apply the harmlessness standard articulated in Brecht v. Abrahamson, 507 U.S. 619, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993). See Sims v. Singletary, 155 F.3d 1297, 1315 (11th Cir.1998). In so doing, we focus on “whether the error had substantial and injurious effect or influence in determining the jury’s verdict.” Id. (quotation marks and citations omitted). For the error not to have been harmless, there must be “more than a reasonable possibility that the error contributed to the sentence.” Horsley v. State of Ala., 45 F.3d 1486, 1493 (11th Cir.1995). 1. The Carol City Trial At the beginning of the sentencing phase of the Carol City trial, the judge told the members of the jury that he later would instruct them as to the mitigation factors that they “may consider.” App. KK, Vol. 4 at 1023. After closing arguments, he stated that “[t]he mitigating circumstances you may consider, if established by the evidence, are these” and then listed the statutory mitigating factors. Id. at 1074-75. He then described the standard of proof for aggravating factors and told the jurors that, although they were limited to considering only the aggravating circumstances he had listed, there was “no such limitation upon the mitigating factors” that could be considered. Id. at 1075. Ferguson contends that he was denied a fair sentencing at the trial because these instructions unconstitutionally precluded the jury from considering non-statutory mitigating evidence in deciding whether to impose the death penalty, in violation of Hitchcock. He asserts that any error from the court’s earlier instructions was not cured by the judge’s later statement indicating that there was no limitation on the mitigating factors. In addition, Ferguson notes that the prosecutor made comments during closing arguments that could be interpreted as supporting the notion that only statutory mitigating factors could be considered. Both the state courts and district court rejected this claim. In the 3.850 proceedings, the Florida Supreme Court found that there had been no Hitchcock error because the trial judge’s later instruction “clearly” informed the jurors “that they were not limited to consideration of the statutory mitigating circumstances.” Ferguson IV, 593 So.2d at 512. Because it made this finding, the court did not address the issue of harmless error. On federal habeas review, the district court determined that the Florida Supreme Court’s statements regarding whether the sentencing judge limited consideration to statutory mitigating factors constituted findings of fact. Since the record supported the Florida Supreme Court’s finding that there had not been such a limitation in the Carol City trial, the court denied Ferguson’s claim. Neither the Florida Supreme nor the federal district court addressed the issue of harmless error. Ferguson maintains that the court’s instructions were contradictory and that the court made no effort to indicate which instruction should control or to explain the discrepancy in its statements. He cites Hall v. Kelso, 892 F.2d 1541, 1545 (11th Cir.1990), for the principle that a later, correct instruction cannot cure an earlier, contradictory instruction in the absence of a clarifying statement by the court. It could be argued that the court’s instructions were more complementary than contradictory, which would make Hall inapplicable here. Under this reading, the court’s initial instruction merely would indicate that jurors could consider the statutory factors described thereafter instead of limiting the jury’s inquiry to solely those factors. The later instruction would inform the jurors that they could consider any non-statutory mitigating factors as well, and thus would have added to the more restrained scope of inquiry suggested by the earlier instruction. Any infirmities in the initial instruction thus would have been cured by the court’s subsequent statement. Nevertheless there are good reasons for declining to adopt that reading. The court’s initial instruction, on its own, clearly would have limited the jury’s consideration to statutory factors and thus violated Hitchcock. See Jones v. Dugger, 867 F.2d 1277, 1279 (11th Cir.1989) (finding Hitchcock error with respect to a virtually identical instruction). Additionally, though the court made a later, non-limiting statement, this “proper instruction was not linked to the erroneous one in such a way as to explicate it or to make clear that the proper instruction was preeminent and controlling.” Hall, 892 F.2d at 1545. Furthermore, the prosecutor’s statements strongly suggested that the jury’s consideration was limited to the statutory factors and therefore “exacerbated the impact of the court’s erroneous instruction.” Jones, 867 F.2d at 1279 n. 4. Bearing all of this in mind, we assume that there was a Hitchcock error here and thus turn to the issue of whether that error was harmless. Ferguson contends that the Hitchcock error was not harmless due to the strength of the mitigating evidence the jury did not consider as a result of the error. In particular, he cites the evidence produced at trial that indicated that the murders were not premeditated, that at least five of the six murders were performed by one of his co-defendants, Marvin Francois, and that he tried to comfort some of the victims. Ferguson contends that the jury reasonably could have concluded from this evidence that he was an unwilling accomplice to Francois’s actions and that he tried to stop the murders. Ferguson also mentions that the jury witnessed his strange behavior at trial, including stripping off his clothes in the courtroom, and that there was evidence at trial regarding his mental problems and prior hospitalization. Additionally, Ferguson asserts that we should consider the cumulative evidentiary effect of the various trial errors, i.e., the mitigating evidence that Robbins failed to produce due to his ineffective assistance as well as the non-statutory mitigating evidence actually produced. As a preliminary note, we cannot consider as part of our harmless error analysis any mitigating evidence that Robbins failed to produce. In performing the harmless error analysis for a Hitchcock claim, we “must consider both the mitigating evidence presented at sentencing as well as mitigating evidence that could have been presented, but which the state trial court prevented the petitioner from presenting.” Smith, 61 F.3d at 817 (quotation marks and citation omitted). “In other words, [we] must consider all potential mitigating evidence that would have been presented, but for the Hitchcock error.” Id. In this case, there is no indication that the trial court inhibited Ferguson’s ability to present the missing mitigating evidence, and Ferguson identifies no case law supporting the notion that a harmless error analysis for a Hitchcock claim should examine such evidence. We thus must determine whether the non-statutory evidence Ferguson actually presented at trial, which he asserts the jury did not consider, would have substantially influenced the outcome if the jury had taken it into account. In fact, the jury may have considered some of this evidence. One of the statutory mitigating circumstances included in the jury instructions was that Ferguson was an accomplice to the offense and played a relatively minor role in its commission. The jury could have viewed evidence regarding Ferguson’s alleged lack of responsibility for the murders in the crime as falling under this category. If this were the case, the only evidence that would have been unconsidered was that respecting the lack of premeditation, which would not be enough to alter the outcome in the face of the aggravating circumstances. Even if we assume that the jury did not take into account any of the evidence Ferguson categorizes as non-statutory, there is good reason to believe that the evidence, had it been considered, would not have altered the outcome of the trial. Notably, we can find only one case, Smith, in which we found that a Hitchcock error was not harmless under the Brecht standard. See Smith, 61 F.3d at 819. The non-statutory evidence in Smith presents a much stronger case for non-harmlessness than does that in Ferguson’s. In Smith, there were at least fourteen different pieces of mitigating evidence that the jury did not consider because of the Hitchcock error. See id. at 817-18. The non-statutory mitigating evidence presented at the Carol City trial also was put forth in Smith, ie., that the defendant did not perform the actual murders, that he was influenced by the dominant personality of an accomplice, and that he had mental difficulties — in Smith, stemming from alcohol and substance abuse. See id. However, in Smith there were a number of other mitigating factors that were not present in Ferguson’s case. For instance, Smith was a minor at the time of the crime, was intoxicated and under the influence of marijuana when the murders occurred, had a non-violent personality, and suffered from epilepsy. See id. Additionally, one of Smith’s accomplices, who had been found guilty of the same number of felonies as Smith, was given a life sentence rather than the death penalty. See id. at 817. Bearing in mind this precedent, we do not believe that there is a reasonable probability that the non-statutory evidence, had it been considered by the jury, would have altered Ferguson’s sentence. Although Smith involved a similar array of aggravating factors, the mitigating circumstances in that case presented a much stronger argument against a death sentence than the mitigating evidence here. Additionally, as previously noted, the aggravating factors here are quite numerous and compelling. Particularly since the jury may have considered much of this mitigating evidence as part of various statutory factors, we do not believe that there was “more than a reasonable possibility that the [Hitchcock] error contributed to [Ferguson’s] sentence.” Horsley, 45 F.3d at 1493. Since the error thus did not have a “substantial and injurious effect or influence in determining the jury’s verdict,” we conclude that it was harmless and that the district court correctly denied Ferguson habeas relief for this claim. Sims, 155 F.3d at 1315 (quotation marks and citations omitted). 2. The Hialeah Trial At the Hialeah trial, the judge’s first two instructions relating to mitigating circumstances were essentially the same as those in the Carol City trial. Unlike in the Carol City proceedings, though, he made no subsequent statement informing the jurors that they were not limited in the mitigating factors they could consider. The parties concede that these instructions constituted a Hitchcock error. We therefore must decide whether this error was harmless under the Brecht standard. The Florida Supreme Court rejected Ferguson’s Hitchcock claim during the 3.850 proceedings. It found that there had been a Hitchcock error in the Hialeah trial but concluded that the error was harmless “beyond a reasonable doubt.” Ferguson IV, 593 So.2d at 513. The court described the additional mitigating evidence presented at the 3.850 hearing, which dealt Ferguson’s family history, as “relatively insignificant.” Id. at 512. It then went on to note that the mitigating evidence was “especially insignificant in light of the heinous nature of the killings in this case and the overwhelming aggravating factors.” Id. The district court agreed that the Hitchcock error “was harmless beyond a reasonable doubt.” R4-108 at 37. In support of this conclusion, the court cited both the egregiousness of the aggravating circumstances and the fact that the jury already had discounted the non-statutory mental health evidence when it considered and rejected Ferguson’s insanity defense. The court also agreed with the Florida Supreme Court that the outcome would have been the same even if the non-statutory mitigating evidence produced at the 3.850 hearing had been taken into account. Ferguson notes that there was a wealth of evidence produced at trial regarding his psychological problems and that he exhibited bizarre behavior during the course of the trial. He asserts that the jury did not consider this evidence in imposing sentence because his counsel presented it only in terms of an insanity defense and did not connect it to a statutory mitigating factor. As previously noted, there is a reasonable argument that the jury did not take the mental health evidence into account because of the language of the jury instructions regarding mental duress and inability to appreciate the impact of one’s actions. See n.24 supra. However, the judge’s instruction to consider and weigh all of the evidence may mitigate the fact that counsel did not connect the evidence to a statutory mitigating factor. Even if we accept Ferguson’s contention that the jury did not consider the evidence, we do not believe that the Hitchcock error would have changed the outcome. The evidence Ferguson cites here is essentially the same as that which he referenced with respect to the prejudice prong of his ineffective assistance claim. In fact, it may even be less since Ferguson has not identified a basis for us to take into account evidence that was not produced at trial. See Smith, 61 F.3d at 817. Since that evidence was insufficient to meet Strickland’s requirement that there be a “reasonable probability” of affecting the outcome, it likewise would not be enough to show the “substantial and injurious effect or influence” on the verdict required under Brecht. Sims, 155 F.3d at 1315 (quotation marks and citations omitted). Furthermore, as in the Carol City case, it is highly improbable that enough jurors would find that the multiple egregious aggravating factors were outweighed by this unconsidered mitigation evidence. We therefore conclude that the Hitchcock error in the Hialeah trial was harmless and that the district court properly denied Ferguson habeas relief with respect to this claim. D. Brady Claim Ferguson contends that the prosecution in both trials violated his due process rights, as described in Brady, by failing to disclose evidence that three of its witnesses, detectives Robert Derringer, Charles Zatrepalek, and Michael MacDonald (“the detectives”), were under investigation for drug trafficking, conspiracy, theft, and civil rights violations. Ferguson asserts that all of the requirements to establish a Brady claim are present here and that the district court erred in failing to grant him habeas relief or, in the alternative, to hold an evidentiary hearing on the issue. He contends that the State possessed evidence of the detectives’ ongoing criminal conduct at the time of the trials because it had constructive, if not actual, knowledge of their illegal activities and the knowledge of the detectives could be imputed to the prosecution. He also maintains that this evidence was material because there were similarities between the charges against Ferguson and the activities in which the detectives were involved, i.e., stealing money from drug dealers and threatening to kill people. According to Ferguson, the prosecution’s failure to provide this evidence undermines confidence in the verdicts because of the critical role the detectives played at trial. The state courts rejected Ferguson’s Brady claim argument during the 3.850 proceedings. The circuit court made three principal findings: (1) that evidence concerning the detectives’ involvement in the illegal activities was not material under the standard articulated in United States v. Bagley, 473 U.S. 667, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985); (2) that the State did not possess the evidence because it had no actual knowledge of the illegal activities and such knowledge could not be imputed to it; and (3) that it was not reasonably probable that the evidence, if admissible, would have changed the outcome of the proceedings. The Florida Supreme Court found the Brady claim to be without merit and dismissed it summarily. The district court determined that Ferguson had failed to state a Brady claim. The court found that each of the circuit court’s three findings could serve as an independent basis for denying Ferguson’s claim. The court agreed that the evidence would have been inadmissible under Florida law and thus was not material for the purposes of assessing the claim. It found that the State did not have possession of the impeachment evidence for the purposes of a Brady violation since it had no actual knowledge of the evidence and the prosecution’s duty to inquire into such evidence would have been trumped by the detectives’ Fifth Amendment rights The court also found that the results of the proceedings would not have changed if the impeachment evidence had been presented. For a petitioner to prevail on a Brady claim, he “must establish (1) the government possessed evidence favorable to him; (2) the defendant did not possess the evidence and could not have obtained it with reasonable diligence; (3) the government suppressed the favorable evidence; and (4) the evidence was material.” Lamarca v. Secretary, Dep’t of Corr., 568 F.3d 929, 941 (11th Cir.2009) (quotation marks and citation omitted). Evidence would be “material” if it is reasonably probable that a different outcome would have resulted if the government had disclosed the evidence. See id. A “reasonable probability” is “a probability sufficient to undermine confidence in the outcome.” Id. (quotation marks and citation omitted). Because we find that the evidence was not material for the purposes of Brady, we need not address the other prongs. The Florida Supreme Court has held that, as a general matter, if a state witness “were presently or recently under actual or threatened criminal charges or investigation leading to such criminal charges,” a defendant has the right to bring out the circumstances behind those charges on cross-examination. Reed v. State, 875 So.2d 415, 431 (Fla.2004) (per curiam) (quotation marks and citation omitted). However, when that “state witness is merely under investigation,” the defendant would not have this right when the investigation is either too remote in time from or not related or relevant to the case at issue. Id. In Breedlove I, we noted that “evidence of unrelated illegal activity by a police officer testifying for the state would likely not have been admissible under Florida’s law of evidence, and thus immaterial for Brady purposes.” Breedlove I, 279 F.3d at 964 (citing Delap, 890 F.2d at 298). Since the detectives had not been charged at the time of Ferguson’s trials, evidence of their illegal activities would have been admissible only if the investigations were related to the cases against Ferguson and were not too remote in time from his trials. We thus must determine whether Ferguson has shown that there was sufficient relation between those investigations and his own case. According to Ferguson, such a connection existed because the detectives were charged with crimes that bore a resemblance to his own. In particular, he cites the fact that the detectives’ crimes involved ripping off drug dealers in the same location and during the same time frame as the Carol City crimes, and that these crimes involved stealing money from a private home and threats to kill people, if not actual killings. See Breedlove I, 279 F.3d at 956. He asserts that these similarities make it distinctly plausible that the detectives had a motivation to resolve Ferguson’s case quickly and possibly to throw suspicion on him for their own crimes. We addressed essentially the same argument in Breedlove I, which involved a Brady claim based on the alleged suppression of evidence regarding illegal activities by many of the same detectives who testified at Ferguson’s trials. See Breedlove I, 279 F.3d at 959-64. In that case, we found it was not objectively unreasonable for the Florida Supreme Court to determine that evidence of the detectives’ crimes was unrelated, and thus not material, to the case against the petitioner, who had been convicted of felony murder connected with a burglary of a house in Miami. See id. at 954-55, 963. Because Breedlove I involved a post-AEDPA inquiry into objective unreasonableness, rather than the de novo review applicable here, our holding in that case would not be binding here. See id. at 963. Even though Breedlove I is not controlling, Ferguson has failed to provide a rationale for us to reach a different conclusion with respect to materiality. The purported connections between Ferguson’s offenses and the detectives’ crimes are too attenuated to meet the materiality test. The criminal scheme in which the detectives took part included a range of drug-related felonies not seen in the Carol City murders, ie., racketeering, possession of various drugs with the intent to distribute, money counterfeiting, and tax evasion. See Alonso, 740 F.2d at 865 n. 1. Additionally, the conspirators used a falsified police warrant to gain entry to the home, a modus operandi distinct from and likely unavailable to Ferguson and his compatriots during the Carol City murders. See id. at 866. The detectives also may not have been aware of the investigations at the time of Ferguson’s trials and thus would not have had a reason to implicate Ferguson for their crimes. See Breedlove v. State, 580 So.2d 605, 607 (Fla.1991) (Breedlove II) (per curiam). If, as Ferguson asserts, the detectives were motivated by a desire to implicate others for their crimes, he has not identified “particular facts” to indicate why the detectives would have had a reason to present false testimony in his specific case. Reed, 875 So.2d at 431. Since Florida courts would have treated such evidence as inadmissible, it is immaterial for Brady purposes. We therefore find that Ferguson has not stated a valid Brady claim and that the district court thus properly denied Ferguson habeas relief for this claim. E. Failure to Correct False Testimony Ferguson also asserts that his due process rights were violated by the prosecution’s eliciting and failing to correct false testimony from Edward Hartmann, a police officer at the Carol City trial. Hartmann testified that Ferguson was convicted of assault with intent to commit murder based on a 1969 shooting incident with Hartmann. In fact, Hartmann shot Ferguson four times, and Ferguson was acquitted of the assault charges, though he was found guilty of robbery in connection with the same incident. Ferguson contends that the prosecutor was aware of this discrepancy and violated his due process rights by failing to correct it. See Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972). He also maintains that his trial and post-conviction counsel were unaware of the error and that his own incompetence prevented him from informing them of it. Ferguson first made this claim in a supplement to his 3.850 motion, which he filed after the circuit court already had denied his motion in full. The circuit court denied his motion to supplement, finding that the motion was untimely because it was “predicated on facts which could have been raised at an earlier time.” App. NN at 1399. The Florida Supreme Court summarily denied Ferguson’s appeal on this issue. The district court found this claim to be procedurally barred under Vining v. State, 827 So.2d 201, 212 (Fla.2002) (per curiam), in which the Florida Supreme Court held that such claims cannot be raised for the first time in a 3.850 motion unless they involved an error that was unknown to the defendant and his counsel at the time of trial and could not be uncovered through due diligence. The district court determined that Robbins was aware of the facts of the shooting incident at the time but did not object to the testimony and that Ferguson’s alleged incompetence could not provide a basis for relief since the circuit court found him competent to stand trial. The court also noted that, even assuming the claim was not procedurally barred, the false testimony amounted to harmless error. To make out a valid Giglio claim, a petitioner “must establish that (1) the prosecutor knowingly used perjured testimony or failed to correct what he subsequently learned was false testimony; and (2) such use was material — i.e., that there is any reasonable likelihood that the false testimony could have affected the judgment.” Davis v. Terry, 465 F.3d 1249, 1253 (11th Cir.2006) (per curiam) (quotation marks, alterations, and citation omitted). Under the then-applicable version of Rule 3.850, a defendant had to file a motion within two years of the date his conviction became final. See Fla. R.Crim. P. 3.850(b) (1990). However, there was an explicit exception to this time bar if the defendant alleged that the facts upon which he based his claim were unknown to him or his attorney “and could not have been ascertained by the exercise of due diligence.” Id. 3.850(b)(1). Furthermore, under that rule, a circuit court was not obligated to consider supplemental pleadings to a 3.850 motion if it had already ruled on the merits of that motion. See id. 3.850(f); State v. Green, 944 So.2d 208, 218 (Fla.2006). The failure to file within the time frame discussed in Rule 3.850 would procedurally bar a petitioner from bringing a federal habeas claim on that issue. See Whiddon v. Dugger, 894 F.2d 1266, 1267-68 (11th Cir.1990). As a preliminary matter, there may have been no Giglio violation here because the prosecutor arguably corrected the false testimony by entering into evidence Ferguson’s correct conviction record, which included a reference to the not guilty verdict; however, no party called attention to the discrepancy. In any event, assuming there was a violation, Ferguson’s claim would be procedurally barred. The motion to supplement was filed twelve years after the completion of trial and a month after the court denied Ferguson’s 3.850 motion. Ferguson’s counsel contends that neither they nor any of his prior counsel had knowledge of the incorrectness of Hartmann’s testimony until July 1990 when they discovered documents indicating a contrary set of events. Even if we accept these facts, and there are reasons to doubt them, Ferguson has not explained why his attorneys could not have obtained evidence of the discrepancy at an earlier date. In light of the extreme time gap between t