JENNIFER WALKER ELROD, Circuit Judge:

In 1993, a Texas jury sentenced Willie Tyrone Trottie to death for the murders of Barbara and Titus Canada. Trottie filed a federal habeas petition pursuant to 28 U.S.C. § 2254, asserting Strickland ineffective-assistance-of-counsel claims, Brady suppression-of-evidence claims, and prosecutorial-misconduct claims. After careful review, the district court denied the petition. Trottie now seeks a certificate of appealability ("COA") pursuant to 28 U.S.C. § 2253(c)(2). For the reasons that follow, we deny Trottie's COA application.

FACTUAL BACKGROUND

Trottie and Barbara Canada met and began dating in about 1989. Shortly thereafter, the two moved in together and had a child. In September 1992, the couple separated and Barbara moved in with her family.

Trottie's behavior towards Barbara became increasingly violent following their 1992 separation. According to state witnesses that testified at Trottie's trial, Trottie warned Barbara that he would kill her if she did not return to him and repeated the threat several times in the months after she moved out. Barbara's close friend testified that Trottie called Barbara "constantly" at home and at work, begging her to come back to him. Trottie hit Barbara, bumped Barbara's car with his own while it was traveling at sixty to sixty-five miles per hour, and once kidnaped her, releasing her only after she promised to reunite with him.

Barbara obtained a protective order against Trottie in March 1993. Nevertheless, state witnesses testified that Trottie telephoned Barbara in April and told her that she had until May 1, 1993 to return to him, or else he would kill her. On May 3, 1993, Trottie called Barbara again and told her that "he wasn't going to wait around anymore" and again threatened to kill her. One witness testified that Trottie also threatened Barbara's brother Titus Canada because, according to Trottie, he had gotten "in the way."

Trottie arrived at the Canada residence at approximately 11:00 p.m. on the night of May 3, 1993, armed with a semiautomatic 9mm pistol.1 At the time, there were five children under the age of seven in the house, along with numerous other family members. According to state witnesses, Trottie opened fire immediately, wounding Barbara's mother, sister, and brother. Barbara's brother returned fire with a .380 caliber pistol and shot Trottie numerous times. Though wounded, Trottie cornered Barbara in a bedroom and, while she lay on the ground, shot her eleven times, saying "Bitch, I told you I was going to kill you." Trottie then returned to the area where Barbara's brother was lying wounded and, in the view of at least two small children, fired two shots into the back of Barbara's brother's head, killing him. Trottie left the Canada home and was arrested a short time later in the emergency room of a nearby hospital.

PROCEDURAL BACKGROUND

The state charged Trottie with the capital murders of Barbara and Titus Canada, and the case went to trial in 1993. The state presented the above-described witness testimony at the guilt/innocence phase of the trial, as well as photographic evidence, testimony by a crime scene investigator, a medical examiner, and a weapons expert. Trottie did not testify, and his counsel did not make a self-defense argument. Rather, Trottie's counsel sought conviction for a lesser-included offense. After hearing the evidence, the jury found Trottie guilty of capital murder.

The case proceeded to the punishment phase. The district court summarized the testimony presented:

Trottie v. Thaler, No. 4:09-CV-0435, 2011 WL 4591975, *1-2 (S.D.Tex. Sept. 30, 2011). Based on this evidence, the jury found that there was a probability that Trottie would commit future acts of criminal violence constituting a continuing threat to society, and that the mitigating evidence was insufficient to warrant a life sentence. Accordingly, the trial court sentenced Trottie to death.

The Texas Court of Criminal Appeals affirmed Trottie's conviction and sentence. Trottie v. State, No. 71,693 (Tex.Crim.App. Sept. 20, 1995). Trottie filed a petition for writ of habeas corpus in the state court in 1997. In 2008, the trial court submitted findings of fact and conclusions of law recommending a denial of habeas relief, which the Texas Court of Criminal Appeals adopted in 2009. Ex Parte Trottie, No. 70,302-01 (Tex.Crim.App. Feb. 11, 2009). Trottie then sought federal habeas relief, which the district court denied in 2011. See Trottie, 2011 WL 4591975, at *1, 20. Trottie now seeks a COA.

STANDARD OF REVIEW

The Antiterrorism and Effective Death Penalty Act of 1996 ("AEDPA") governs Trottie's habeas petition. Under AEDPA, a state court prisoner must obtain a certificate of appealability ("COA") before he can appeal a federal district court's denial of habeas relief. 28 U.S.C. § 2253(c)(1)(A). A COA is warranted upon a "substantial showing of the denial of a constitutional right." Id. § 2253(c)(2). A petitioner satisfies this standard if "reasonable jurists would find the district court's assessment of the constitutional claims debatable or wrong." Slack v. McDaniel, 529 U.S. 473, 484, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000); see Miller-El v. Cockrell, 537 U.S. 322, 327, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003).2 The issue is "the debatability of the underlying constitutional claim, not the resolution of that debate." Miller-El, 537 U.S. at 342, 123 S.Ct. 1029. "This threshold inquiry does not require full consideration of the factual or legal bases adduced in support of the claims. In fact, the statute forbids it." Id. at 336, 123 S.Ct. 1029. In cases involving the death penalty, "any doubts as to whether a COA should issue must be resolved in [the petitioner's] favor." Hernandez v. Johnson, 213 F.3d 243, 248 (5th Cir.2000) (citation omitted).

We evaluate the debatability of Trottie's constitutional claims under AEDPA's highly deferential standard, which "demands that state-court decisions be given the benefit of the doubt." Renico v. Lett, 559 U.S. 766, 130 S.Ct. 1855, 1862, 176 L.Ed.2d 678 (2010) (citations and internal quotation marks omitted). Under AEDPA, a federal court may not grant habeas relief unless the petitioner has first exhausted state remedies with respect to the claim at issue. 28 U.S.C. § 2254(b). To prevail, a habeas petitioner must prove that the constitutional adjudication by the state court "resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States," 28 U.S.C. § 2254(d)(1), or "resulted in a decision that was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding," § 2254(d)(2).3 Clearly established federal law is comprised of "the holdings, as opposed to the dicta, of [the Supreme] Court's decisions as of the time of the relevant state-court decision." Williams v. Taylor, 529 U.S. 362, 412, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). A state court decision is contrary to clearly established federal law when it "arrives at a conclusion opposite to that reached by [the Supreme Court] on a question of law or if the state court decides a case differently than [the Supreme Court] has on a set of materially indistinguishable facts." Id. at 413, 120 S.Ct. 1495. A state-court decision fails the "unreasonable application" prong if it "identifies the correct governing legal rule from [the Supreme Court's] cases but unreasonably applies it to the facts of the particular state prisoner's case," id. at 407, 120 S.Ct. 1495, or when it "extends a legal principle from [Supreme Court] precedent to a new context where it should not apply or unreasonably refuses to extend that principle to a new context where it should apply," id.

That a federal habeas court would reach a different conclusion is not enough, standing alone, to merit relief under AEDPA's high standard. See id. at 411, 120 S.Ct. 1495. As the Supreme Court recently reiterated, "even a strong case for relief does not mean the state court's contrary conclusion was unreasonable." Richter, 131 S.Ct. at 786. We defer to the state trial court's factual findings, Moody v. Quarterman, 476 F.3d 260, 267-68 (5th Cir.2007), and consider only the record that was before the state court, Cullen v. Pinholster, ___ U.S. ___, 131 S.Ct. 1388, 1398, 179 L.Ed.2d 557 (2011). We review only the ultimate legal determination by the state court — not every link in its reasoning. Neal v. Puckett, 286 F.3d 230, 246 (5th Cir.2002) (en banc); see Catalan v. Cockrell, 315 F.3d 491, 493 (5th Cir.2002). In reviewing a state court habeas decision reached without explanation, "a federal court must `determine what arguments or theories ... could have supported the state court's decision,' and then ask `whether it is possible fairminded jurists could disagree that those arguments or theories are inconsistent with the holding in a prior decision' of the Supreme Court." Williams v. Thaler, 684 F.3d 597, 603 (5th Cir.2012) (quoting Richter, 131 S.Ct. at 786).

DISCUSSION

Trottie asserts three theories of habeas relief: (1) ineffective assistance of counsel, (2) Brady violations, and (3) prosecutorial misconduct. The district court's well-reasoned conclusions on these three theories are not debatable, and we conclude that a COA should not issue. We address each theory in turn.

I. Ineffective Assistance of Counsel

Trottie's ineffective assistance of counsel claims are subject to the standard set forth in Strickland v. Washington:

466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). To establish deficient performance, "the defendant must show that counsel's representation fell below an objective standard of reasonableness." Id. at 688, 104 S.Ct. 2052. In evaluating deficiency, we apply a "strong presumption that counsel's conduct falls within the wide range of reasonable professional assistance." Id. at 689, 104 S.Ct. 2052. Strickland's second prong "focuses on the result of counsel's deficient performance: `When a defendant challenges a death sentence..., the question is whether there is a reasonable probability that, absent the errors, the sentencer ... would have concluded that the balance of aggravating and mitigating circumstances did not warrant death.'" Roberts v. Thaler, 681 F.3d 597, 610 (5th Cir.2012), cert. denied, ___ U.S. ___, 133 S.Ct. 529, 184 L.Ed.2d 345 (2012) (quoting Strickland, 466 U.S. at 695, 104 S.Ct. 2052). A reasonable probability is "a probability sufficient to undermine confidence in the outcome." Strickland, 466 U.S. at 694, 104 S.Ct. 2052. Prejudice exists when the likelihood of a different result is "substantial, not just conceivable." Richter, 131 S.Ct. at 791-92.

When an ineffective-assistance-of-counsel claim is subject to AEDPA, "the pivotal question is whether the state court's application of the Strickland standard was unreasonable." Id. at 785. The Supreme Court has explained:

Id. Thus, while "[s]urmounting Strickland's high bar is never an easy task," "establishing that a state court's application of Strickland was unreasonable under § 2254(d) is all the more difficult." Id. at 788 (citations omitted). Both the Strickland standard and the AEDPA standard are "highly deferential" and "when the two apply in tandem, review is `doubly' so." Id. (citations omitted). With this precedent in mind, we first turn to what Trottie calls the "heart" of his ineffective-assistance claim: trial counsel's alleged failure to investigate and present additional witnesses at the guilt/innocence and punishment phases of his trial.

A. Failure to Investigate and Present Additional Witnesses4

Particularly in the context of a capital case, defense counsel has the obligation to conduct a "reasonably substantial, independent investigation." Neal v. Puckett, 239 F.3d 683, 688 (5th Cir.2001) (quoting Baldwin v. Maggio, 704 F.2d 1325, 1332-33 (5th Cir.1983)). The Supreme Court has explained the governing standard:

Strickland, 466 U.S. at 690-91, 104 S.Ct. 2052; see also Williams v. Taylor, 529 U.S. 362, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000); Wiggins v. Smith, 539 U.S. 510, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003); Rompilla v. Beard, 545 U.S. 374, 125 S.Ct. 2456, 162 L.Ed.2d 360 (2005). There are no "strict rules" for counsel's conduct beyond "the general requirement of reasonableness." Pinholster, 131 S.Ct. at 1406-07. "An attorney need not pursue an investigation that would be fruitless, much less one that might be harmful to the defense." Richter, 131 S.Ct. at 789-90 (citing Strickland, 466 U.S. at 691, 104 S.Ct. 2052). Trial counsel is "entitled to formulate a strategy that was reasonable at the time and to balance limited resources in accord with effective trial tactics and strategies." Id. at 789. Moreover, "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." Druery v. Thaler, 647 F.3d 535, 541 (5th Cir.2011), cert. denied, ___ U.S. ___, 132 S.Ct. 1550, 182 L.Ed.2d 180 (2012) (quoting Nelson v. Hargett, 989 F.2d 847, 850 (5th Cir.1993)).

Upon a reasonable investigation, defense counsel also has an obligation to make reasonable strategic decisions regarding which witnesses and evidence he will present. Cf. Strickland, 466 U.S. at 690-91, 104 S.Ct. 2052. "[T]he failure to present a particular line of argument or evidence is presumed to have been the result of strategic choice." Taylor v. Maggio, 727 F.2d 341, 347 (5th Cir.1984). As we have held, "a tactical decision not to pursue and present potential mitigating evidence on the grounds that it is double-edged in nature is objectively reasonable, and therefore does not amount to deficient performance." Rector v. Johnson, 120 F.3d 551, 564 (5th Cir.1997).

Trottie bases his primary ineffective-assistance-of-counsel claim on his trial counsel's failure to both investigate and present additional witnesses. We address these issues in tandem below, as they depend on a nearly identical analysis here.

1. Deficiency

In his state-court petition, Trottie argued that his trial counsel "ignored" "obvious and available" defenses — most importantly, self-defense — and failed to present "important, competent, and available evidence" of mitigation. This is, Trottie now emphasizes, a function of his trial counsel's inadequate investigation of the case and preparation for trial. According to an affidavit that Trottie submitted to the state court, he met with Connie Williams, his lead counsel, only twice before the day of trial, for less than an hour total. Trottie met with a private investigator obtained by his counsel, but contends that "very little was discussed." And Trottie says that, although he provided Williams with the names of numerous potential witnesses, Williams failed to contact and interview them. The witnesses that Williams did contact and ultimately call to testify, he allegedly failed to prepare. An affidavit by Trottie's sister, submitted to the state court, indicates that she "did not know what [she] would be testifying to or what phase of the trial [she] would be needed for." It further states: "I wanted to offer more relevant information on behalf of my brother as [far] as mitigation, and his character ... However, I wasn't asked about these topics."

Williams tells a different story. His affidavit, also submitted in the course of the state habeas proceeding, indicates that he: "prepared and filed pre-trial motions; interviewed witnesses; obtained discovery from the State; reviewed the State's file; researched the applicable law concerning Trottie's case; and, talked with Trottie numerous times about the offense, the pending trial, and potential defense witnesses." Williams hired a private investigator, who purportedly interviewed Trottie's parents and thirteen other potential witnesses, and a psychiatrist, who testified on Trottie's behalf after performing a psychological examination.

Ultimately, the scope of Williams's investigation and preparation for trial boils down to a credibility dispute, one the state court resolved against Trottie. It found Williams's affidavit "credible," and relied on it extensively in rejecting Trottie's habeas claim. The state court credited Williams with numerous strategic decisions, including the decision not to call certain witnesses and not to present a self-defense argument.5 We must defer to the state court's factual findings, and deny relief "if there is any reasonable argument that counsel satisfied Strickland's deferential standard." Richter, 131 S.Ct. at 788 (emphasis added). As the district court noted, there is sufficient record evidence here to support the state court's conclusion that Williams's investigation and preparation for trial was not deficient.6 Because reasonable jurists would not debate the district court's view, a COA is not warranted.

2. Prejudice

Even if Williams's failure to investigate and present the additional witnesses had been deficient, the state court determined that Trottie could not show prejudice: the purportedly missing testimony was either insufficiently described, cumulative, or strategically omitted by Trottie's counsel. Because we conclude that there is no debate that the state court's decision was reasonable, a COA is not warranted for this additional reason.7

Trottie submitted seven affidavits in the course of his state habeas proceeding: four alongside his initial petition in 1997 and three alongside his proposed findings of fact and conclusions of law in 2008. The 1997 affidavits consisted of testimony by: Jim L. Peacock, Trottie's attorney at the time8; Theotis Holmes and Tonya Baul, potential character witnesses who were subpoenaed but never testified; and George Uthe, a private investigator with information regarding statements by Patrice Espree, another potential witness who was subpoenaed but never testified. The affidavits of Holmes, Baul, and Uthe all included similar language indicating that the potential witness possessed information regarding whether Trottie was a continuing threat to society, Trottie's emotional and mental state at the time of the incident (which "impair[ed] his ability to rationally handle the situation"), and the "events leading up to Mr. Trottie's arrival at Barbara Canada's home on May 3, 1993[,] which would have shown the immense strain on the relationship between Mr. Trottie and the decedents at the time...." The 2008 affidavits consisted of testimony by: Trottie himself regarding what he would have said had he been called to the stand9 and a list of uncalled witnesses with relevant information10; Trottie's father, who wished to testify regarding his son's relationship with Barbara and good character; and Trottie's sister, who testified but wanted to offer additional testimony regarding her brother's childhood, relationship with Barbara, and good character.

The state court found each of these affidavits "unpersuasive." In reaching its conclusion, the state court explained that: (1) the affidavits offered insufficient detail regarding the specific testimony that would have been elicited at trial; (2) Trottie failed to show that they were not cumulative of testimony already elicited at trial; and (3) the potential witnesses could not testify regarding the instant offense or the applicant's potential defenses because they were not present at the time of the incident.11 In addition, the state court specifically noted that defense counsel made the strategic decision not to call certain witnesses, namely Holmes, Baul, and Espree, based on his assessment that their testimony would not benefit the defense. On this basis, the state court reasonably rejected Trottie's ineffective-assistance claim.

Trottie contends that two specific categories of evidence would have made a difference in his case. First, with respect to the guilt/innocence phase of the trial, Trottie argues that Williams failed to present evidence that would have undermined the jury's conclusion that he premeditated the murders of Barbara and her brother. For example, Trottie argues that many of the above-listed witnesses would have testified that he and Barbara had an ongoing romantic relationship, and that they continued to communicate even after Barbara obtained a protective order against Trottie.12 Trottie further argues that the testimony would have established that Barbara's brother shot at him first, which supports a theory of self-defense.

With regard to Trottie's relationship with Barbara, the district court summarized the state court's findings as follows:

Trottie, 2011 WL 4591975, at *11 (internal citations omitted).13

Likewise, with respect to whether Barbara's brother, not Trottie, fired the first shot, the district court stated:

Id. at *14.14 Thus, the district court determined that the "witnesses that Trottie now claims counsel should have called [at the guilt/innocence phase of the trial] would have been cumulative of the evidence in the record." Our review of the record confirms that reasonable jurists would not debate this conclusion.

Second, Trottie argues that his counsel should have investigated and presented additional mitigation evidence at the punishment phase of the trial. Specifically, Trottie asserts that numerous witnesses would have testified to the "horrors that [he] experienced as a child." Trottie's state habeas filings, however, offer no detail regarding the purportedly missing testimony. Although Trottie attempted to address this problem in his federal habeas petition, filing new affidavits from several relatives, Pinholster forecloses our review of that evidence. See Pinholster, 131 S.Ct. at 1398.15

We note that Trottie's counsel did present some evidence regarding Trottie's difficult childhood at the sentencing phase of the trial. This testimony included a description of Trottie's abandonment at a motel doorstep, placement in foster care, abuse while in foster care, and repeated attempts to run away to find his mother or grandmother.16 In addition, the psychiatrist that examined Trottie prior to trial testified that Trottie's abandonment by his mother may have played a part in his violent reaction to Barbara's rejection. She said: "I think the issue of his abandonment and rejection by a woman in his very early life, his mother, predisposed him to be sensitized to that issue such that he might do well in situations where that wasn't a factor but he may react very strongly to times of being rejected, abandoned again...." Thus, although the jury may not have had all of the facts that Trottie now wishes it had, Trottie's counsel did offer meaningful information regarding Trottie's childhood and how it may have impacted Trottie's decisions on the day of the incident.

In short, the district court concluded that Trottie was not entitled to habeas relief based on Williams's purported failure to investigate and present additional witnesses. Having reviewed the affidavits and trial court record, and considering the deference owed to the state court, there is no debate that the state court's decision was reasonable. Thus, a COA is not warranted with regard to this claim.

B. Additional Grounds for Trottie's Ineffective-Assistance Claims

1. Failure to Provide Guidance in Psychological Evaluations

In his federal habeas petition, Trottie asserts that his counsel failed to provide him with any guidance regarding his competency and sanity evaluations; according to Trottie, "[c]ounsel's deficiency in this regard was disastrous ... the State used Trottie's statements to develop its preemptive counter-theory of planning and premeditation." Trottie, however, failed to raise this issue in the state habeas proceedings. Thus, we agree with the district court that this factual basis for Trottie's ineffective-assistance claim is unexhausted and procedurally defaulted. Moreover, even if Trottie had exhausted the claim, the district court concluded that Trottie could not show prejudice, as "[n]othing in the record supports Trottie's speculative claim that statements he made during the evaluations led to the State's theory of the case." Trottie, 2011 WL 4591975, at *10. Because reasonable jurists would not debate the district court's decision on either ground, a COA is not warranted on this issue.

2. Failure to Rebut Extraneous Offense Evidence

The state relied on evidence of two prior uncharged offenses to demonstrate Trottie's future dangerousness. Specifically, it presented evidence that Trottie: (1) was involved in a shootout with another man in 1990 and (2) pulled a gun on a man named Frederick Rusk, the father of Barbara's daughter, while in front of the Canada house. Trottie's state habeas affidavit is silent with respect to the second incident, and it is therefore unexhausted and procedurally defaulted.17 Regarding the alleged "shootout," Trottie's state habeas petition focused on his counsel's failure to properly object to this evidence, not his failure to rebut it. The state habeas court ultimately rejected this argument, noting that the objection would have been properly overruled if made. In addition, the affidavit that Trottie submitted to the state court in 2008 indicated that, had he testified, he would have explained that "it was not evidence of a violent nature or a previous violent criminal act on [his] behalf." Because the state court reasonably concluded that Williams's failure to call Trottie to the stand was neither deficient nor prejudicial, as discussed in footnote 9 above, this proposed evidence does not merit habeas relief. Thus, there is no debate that the state court's decision was reasonable.

We note that Trottie submitted new affidavits with his federal habeas claim, which include information regarding both of the extraneous offenses. The district court concluded that the affidavits were unexhausted and foreclosed from review by Pinholster. Trottie, 2011 WL 4591975, at *6-7. We agree. In addition, the district court determined that the affidavits failed to show prejudice on the merits:

Id. at *13. Because the district court's conclusions are not debatable, a COA is not warranted.

3. Failure to Address Inconsistencies in the State's Evidence

Trottie's federal habeas petition asserts that Trottie's counsel should have addressed several alleged inconsistencies in the State's case, primarily related to the details of the crime. These details include the placement of shattered glass at the front door of the Canada residence, the range from which Trottie shot Barbara's brother, and the number of shots that Trottie fired at Barbara's brother. Although Trottie's state petition asserted that Trottie's counsel should have retained ballistics and blood spatter experts to testify regarding some of these issues, Trottie did not articulate specific inconsistences in the trial testimony until he filed his federal habeas petition. Thus, the district court's conclusion that these arguments are unexhausted and barred by Pinholster is not debatable. See Trottie, 2011 WL 4591975, at *6-7. Moreover, the district court carefully and correctly explained why Trottie's new evidence is insufficient to warrant habeas relief. Id. at *13-14. In short, it concluded that there is no reasonable probability that the rebuttal evidence would have affected the outcome of Trottie's trial. Id. Reasonable jurists would not disagree with the district court on either ground.

4. Failure to Address Trottie's Wardrobe

Trottie also contends that his counsel should have rebutted evidence that he wore an all-black outfit to the Canada residence, from which the state implied that he premeditated the murders of Barbara and her brother. In his state habeas proceeding, Trottie asserted that — had his counsel called him to testify — he would have said that he wore black not because he planned to harm anyone, but because he "virtually always" dressed that way. This claim fails on both Strickland prongs: (1) Trottie cannot, and does not seek to, demonstrate deficiency in his counsel's failure to call him to testify, see supra footnote 9, and (2) the state presented evidence that Trottie also wore a ski mask, which greatly undermines Trottie's ability to show prejudice. The district court's rejection of this factual basis is not debatable.18

C. The Impact of the Texas Capital Murder Statute

Throughout his COA application — and particularly with respect to his Strickland claims — Trottie argues that the state and district courts misunderstood the Texas capital murder statute, Texas Penal Code § 19.03(a)(6)(A) (1993). At the time of Trottie's trial, the statute provided that a person committed a capital offense if he (a) intentionally or knowingly (b) caused the deaths of (c) two or more individuals (d) during a single criminal transaction. See Trottie v. State, No. 71,693 (Tex.Crim. App. Sept. 20, 1995).

Trottie contends that the proposed witness testimony would have cast reasonable doubt on whether he intended to murder both Barbara and her brother following planning and premeditation. According to Trottie, "the uncalled witness testimony, considered together with inconsistencies among witness testimony and forensic evidence at trial, contravenes the State's theory of planning and premeditation." Rather, "it establishes the ongoing, romantic nature of Barbara's relationship with Trottie and serves to confirm the alternate theory that Barbara's brother fired the first shot rather than Trottie." This amounts to either a sufficiency-of-the-evidence argument or an actual innocence claim, neither of which Trottie clearly articulates. In any event, the state appellate court rejected this argument in the course of Trottie's direct appeal. Id. at 3-4. It stated:

Id. The state appellate court further concluded that the evidence "did not raise the possibility that [Trottie] killed his victims out of sudden passion arising from adequate cause." Id. at 4. With this reasonable conclusion in mind, Trottie's argument regarding the Texas capital murder statute is unavailing.

To summarize, the district court carefully considered every factual and legal basis for Trottie's ineffective-assistance claim, and determined that it either (1) was unexhausted and procedurally defaulted, (2) was reasonably rejected by the state court, or (3) failed on the merits.19 Because reasonable jurists would not debate the district court's conclusions, we will not grant a COA on any of Trottie's Strickland claims.

II. Alleged Brady Violations

In addition to his ineffective-assistance-of-counsel claims, Trottie contends that the State suppressed favorable statements it obtained in investigating Trottie's case. To establish a Brady violation, Trottie must prove that (1) the prosecution actually suppressed the statements, (2) the statements were favorable to Trottie, and (3) the statements were material. United States v. Brown, 650 F.3d 581, 587-88 (5th Cir.2011), cert. denied, ___ U.S. ___, 132 S.Ct. 1969, 182 L.Ed.2d 833 (2012) (citations omitted). Suppression exists only where a defendant did not — and could not — know about the essential facts that would enable him to take advantage of the evidence. Id. at 588 (citations omitted). Thus, a defendant cannot succeed on a Brady claim if he could have discovered the evidence through reasonable due diligence. Id. (citations omitted). Materiality exists if there is "`a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different.'" Id. (quoting United States v. Bagley, 473 U.S. 667, 682, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985)). As with the prejudice standard that governs ineffective-assistance-of-counsel claims, the "likelihood of a different result must be substantial, not just conceivable." Id. (quoting Richter, 131 S.Ct. at 792). A "reasonable probability" is less than "`more likely than not,'" but the difference "is slight and matters `only in the rarest case.'" Id.

Trottie claims that the state prosecutor violated Brady when he failed to disclose Trottie's former probation officer's statement that Barbara "probably did mess with [Trottie's] head a little."20 As the district court noted, Trottie raised this claim for the first time in his federal habeas petition. According to Trottie, this is because he first learned about this evidence when the Houston County District Attorney's Office turned over its work product in the course of his federal habeas proceeding.

The district court rejected Trottie's Brady claim on two grounds. First, it held that Trottie failed to demonstrate suppression: "Trottie makes no showing that appellate or state habeas counsel ever sought the State's file. There is therefore no reason to believe that this information was not readily available to Trottie throughout his legal proceedings, no evidence of suppression, and no cause for his procedural default." Trottie, 2011 WL 4591975, at *15. We agree. In fact, a November 15, 1993 note in the prosecutor's file states: "Connie Williams & Elizabeth spent several afternoons looking at the file. Kate Dolan also always had the file open to the defense." Likewise, Williams's affidavit, submitted to the state habeas court, indicates that he "obtained discovery from the State" and "reviewed the State's file." Although Trottie speculates that the note at issue was not contained within the file when Williams reviewed it, he offers no evidence on this point. Thus, Trottie cannot meet his burden to show suppression. See United States v. Edwards, 442 F.3d 258, 267 n. 9 (5th Cir.2006) (explaining that the party alleging a Brady violation bears the burden of establishing all three prongs of the Brady test (citation omitted)); see also Medellin v. Dretke, 371 F.3d 270, 281 (5th Cir.2004) (declining to issue a COA regarding a Brady claim that depended upon a "substantial degree of speculation"); Hughes, 191 F.3d at 629-30 (holding that speculation of suppression is insufficient to establish a Brady claim).

Even assuming that the State failed to disclose the note, the district court rightly concluded that Trottie could not show materiality, stating that "[o]ther witnesses testified about Trottie's relationship with Barbara" and calling the purportedly suppressed evidence "at best, cumulative." See Trottie, 2011 WL 4591975, at *16. This conclusion is not debatable, especially in light of defense counsel's closing arguments at the guilt/innocence phase of Trottie's trial. Williams emphasized that Barbara willingly continued her relationship with Trottie, even after obtaining a protective order against him: "[w]e know that Barbara ... chose to not follow that protective order"; "she came to him on many occasions"; "[Trottie] was almost invited to [disobey the protective order] by the frequent contact that you heard the witnesses testify to." Thus, whether or not the State disclosed the note, there is no reasonable dispute that the defense — and the jury — knew about Trottie's back-and-forth relationship with Barbara. There is no debate that Trottie fails to demonstrate a reasonable probability that, had the statement been disclosed to the defense, the result of the proceeding would have been different. Accordingly, Trottie is not entitled to a COA regarding his Brady claim.21

III. Prosecutorial Misconduct

Finally, Trottie argues that the state prosecutor's misconduct — specifically, his repeated reference to certain tape recordings after they were excluded from evidence — infected his trial.22 We analyze prosecutorial-misconduct claims in two steps. United States v. Ebron, 683 F.3d 105, 140 (5th Cir.2012) (citation omitted). First, we evaluate whether the prosecutor made an improper remark. United States v. Fields, 483 F.3d 313, 358 (5th Cir.2007) (citation omitted). If so, then we determine whether the defendant suffered prejudice. Id. (citation omitted). "The prejudice step of the inquiry sets a high bar: `Improper prosecutorial comments constitute reversible error only where the defendant's right to a fair trial is substantially affected.'" Ebron, 683 F.3d at 140 (quoting United States v. Holmes, 406 F.3d 337, 355-56 (5th Cir.2005)). Thus, a criminal conviction should not be "lightly overturned on the basis of a prosecutor's comments standing alone." Id. Rather, "the determinative question is whether the prosecutor's remarks cast serious doubt on the correctness of the jury's verdict." Id. In deciding whether serious doubt infects the verdict, we look to three factors: "(1) the magnitude of the prejudicial effect of the prosecutor's remarks, (2) the efficacy of any cautionary instruction by the judge, and (3) the strength of the evidence supporting the conviction." Id. (quoting United States v. Mares, 402 F.3d 511, 515 (5th Cir.2005)) (internal quotation marks omitted). We generally review occurrences of prosecutorial misconduct individually, but there "may be instances where improper statements, which are not individually prejudicial enough to require reversal, could cumulate to affect the defendant's substantial rights." Fields, 483 F.3d at 358 (quoting United States v. Wicker, 933 F.2d 284, 292 (5th Cir.1991)). Such instances, however, "are rare." Id. (quoting Wicker, 933 F.2d at 292). "To warrant a new trial, prosecutorial misconduct must be `so pronounced and persistent that it permeates the entire atmosphere of the trial.'" United States v. Jimenez, 509 F.3d 682, 691-92 (5th Cir.2007) (quoting United States v. Wyly, 193 F.3d 289, 299 (5th Cir.1999)).

Because this case is subject to AEDPA, our prosecutorial-misconduct analysis is subject not only to the "high bar" discussed above, but also to the deference that we afford to the state habeas court's decision. Cf. Richter, 131 S.Ct. at 786-87. Trottie is not entitled to habeas relief unless the state court's decision was contrary to, or an unreasonable application of, clearly established federal law. See 28 U.S.C. § 2254(b). Thus, we ask not whether the state court reached the correct decision, but rather a reasonable one. Richter, 131 S.Ct. at 785 (explaining that "an unreasonable application of federal law is different from an incorrect application of federal law" (citation omitted)).

At issue here is the state's reference to certain tape-recordings that the trial court deemed inadmissible. The recordings captured phone conversations between Trottie and Barbara, in which Trottie purportedly threatened her. The trial court held a hearing outside of the presence of the jury to determine the admissibility of the tape recordings and, at the conclusion of the hearing, sustained Trottie's objection. Later, in the presence of the jury, the state again attempted to introduce the tapes. Defense counsel objected, stating: "It's my understanding the Court already ruled on the tapes." After some discussion at the bench, the trial court advised the prosecutor to "stay away" from the subject of the tapes and "go on to something else." Very shortly thereafter, the prosecutor asked the same witness yet another question about the tapes ("[w]as any of that stuff tape recorded?"). Trottie's defense counsel objected and moved for a mistrial. The court denied the motion for a mistrial, but instructed the jury to "disregard the last question and do not consider it for any purpose whatsoever."

The jury sent two notes regarding the tapes in the course of its guilt/innocence deliberations. The first note sought numerous pieces of evidence, much of which had been admitted into evidence, including "pictures, tapes, [and an] autopsy report." In an itemized list, the jury specifically requested "cassette tapes." The jury's second note sought exclusively the "tape recordings of threats," along with a tape recorder. The court responded: "not in evidence." Trottie relies on these notes to illustrate the importance of the cassette tapes in the minds of the jurors.

Despite the court's response to the jurors' second note, the prosecutor mentioned the tapes again during the punishment phase of the trial. The following exchange occurred during cross-examination of the psychiatrist that testified on Trottie's behalf:

The court denied defense counsel's request for a mistrial.

Recognizing a litigant's duty to afford great respect to a trial court's evidentiary rulings — especially when speaking in front of a jury — we assume, arguendo, that the prosecutor's statements were improper. Thus, we turn to the second prong of the prosecutorial-misconduct inquiry: whether the statements substantially affected Trottie's right to a fair trial. The district court concluded that they did not:

See Trottie, 2011 WL 4591975, at *17.23 This conclusion is not debatable. Trottie offers no more than speculation that the court's curative instructions and its response to the jury note were insufficient to neutralize the prosecutor's statements. Moreover, as the district court noted, the evidence that was admitted established — over and over again — that Trottie threatened Barbara's life. Indeed, one witness's testimony included a long exchange regarding the tapes, to which defense counsel did not object. The testimony included the following:

Thus, much of the purported content of the tape recordings was cumulative of the evidence already in the record. Accordingly, reasonable jurists would not debate the reasonableness of the state habeas court's decision, and a COA is not warranted.

CONCLUSION

For the reasons stated above, we conclude that reasonable jurists would not debate the district court's conclusions regarding any of Trottie's Strickland, Brady, and prosecutorial-misconduct claims, and Trottie therefore makes no substantial showing of the denial of a constitutional right. Accordingly, we DENY Trottie's COA application.