Perry Eugene Williams (“Williams”) appeals the district court’s denial of habeas relief from his death penalty sentence following a 2002 state court conviction for capital murder. Because of an intervening change in the law, Williams brought a Federal Rule of Civil Procedure 59(e) motion regarding his first claim — whether trial counsel rendered constitutionally ineffective assistance by failing to investigate and present certain mitigating evidence. The district court originally denied relief on this claim as procedurally defaulted. Upon reconsideration, the district court again denied relief, but granted a certificate of appealability (“COA”) on this issue. Williams appeals this ruling. Additionally, Williams seeks to expand the COA as to the following issues: (1) whether trial counsel was ineffective at the punishment stage of the trial for failing to present mitigation evidence of Williams’s substance abuse; and (2) whether the state trial court violated Williams’s Due Process and Eighth Amendment rights by excluding the statement of an accomplice, James Dunn, at the punishment phase. For the reasons set forth below, we AFFIRM the district court’s Rule 59 ruling and DENY a COA on the other two issues.
I. Background
Williams was convicted of murdering Matthew Carter during a multi-day crime spree that involved several armed robberies and the shooting of two other individuals. On the night in question, Williams and his codefendants went to the parking lot of a Blockbuster video store. After being handed a pistol and told to “go get 'em” (referring to Carter), Williams exited the car, brandished the pistol, and told Carter to get in Carter’s car. After driving awhile, they pulled into a parking lot, at which point Carter attempted to escape the car, and he pushed or jostled Williams. At this point, the gun went off (Williams alleges this was by accident, the State alleges it was intentional), with a single shot fatally striking Carter in the head. Williams and his codefendants then took items from Carter and attempted to eliminate evidence. Thereafter, they continued their crime spree by robbing and shooting another individual. Evidence along these lines was presented at Williams’s trial, and the jury convicted him of capital murder. Williams does not seek habeas relief from this conviction.
In preparation for trial, Williams’s trial counsel, Robert Morrow, retained Dr. Gilda Kessner, a licensed psychologist, to evaluate Williams. She prepared a report that contained information on Williams’s background, drug use, and family members, including that his father served in Vietnam and was diagnosed with post-traumatic stress disorder (“PTSD”). The report explained Williams’s extensive substance abuse and Dr. Ressner’s opinion that “[wjithout the drugs, [it is] highly unlikely that he would have engaged in [criminal] behavior.”
Morrow explained his strategy at the punishment phase in an affidavit submitted in Williams’s state habeas case by stating that he sought to emphasize the “positive aspects” of Williams’s life and contrast those with the “limited, although very serious,” days of the crimes in question. He wanted the jury to conclude that “Williams was a great deal more than the offenses *383the jury had heard about.” Pursuant to this strategy, Morrow offered testimony from ten individuals, including family, friends, and other individuals who knew Williams. See Williams v. State, 273 S.W.3d 200, 208 (Tex.Crim.App.2008) (describing the mitigation testimony). Williams’s mother testified that he was raised in a close-knit, religious family. She testified favorably regarding Williams’s relationship with his father, who was a truck driver and veteran. She also mentioned some of the family’s difficulties: she had cancer; her mother died of cancer; her sister was murdered; two of Williams’s cousins were murdered; and her father suffered a stroke.
Morrow also explained that he “felt [Williams] would make a strong witness at punishment. By accepting responsibility and expressing remorse it was [counsel’s] hope the jury would see the Perry Williams that [they] saw every day.” Pursuant to this strategy, Morrow elicited from Williams repeated testimony that he was not blaming his actions on his drug use, his family, or anyone else; that he was responsible for Carter’s death; and that he was the only person responsible for his actions. See id. at 208-11. Accordingly, Morrow did not present Dr. Kessner’s testimony because it contradicted his strategy of emphasizing the positive aspects of Williams’s life and having Williams accept responsibility for his actions. The jury sentenced Williams to death.
Williams appealed his conviction and sentence, challenging, inter alia, the trial court’s exclusion of the statement of an accomplice, James Dunn, at the punishment phase of the trial, but the Texas Court of Criminal Appeals (“CCA”) affirmed. Id. at 231-33, 235. Williams then filed a state habeas application, asserting, among other things, an ineffective assistance of counsel (“LAC”) claim based on trial counsel’s alleged failure to present evidence of Williams’s drug abuse and expert testimony on that drug abuse. The state habeas court issued findings of fact and conclusions of law recommending the CCA deny habeas relief. The CCA adopted the findings of fact and conclusions of law and denied relief. Ex parte Williams, Nos. WR-63237-01,-02, 2008 WL 5050078 (Tex.Crim.App. Nov. 26, 2008) (unpublished).
Williams then sought relief in federal court, asserting the two grounds raised in his direct appeal and state habeas case. Williams further asserted, as his first claim, a ground arguably not raised in state court — that counsel was ineffective at the punishment phase of the trial by failing to conduct a thorough social history investigation and failing to present additional social history evidence as mitigation. Williams admitted that this first claim was unexhausted in state court. The district court stayed the case, and Williams asserted his first claim in a state habeas application, which was dismissed as an abuse of the writ. Ex parte Williams, No. WR-63237-03, 2010 WL 4523789 (Tex.Crim.App. Nov. 10, 2010) (unpublished).
Thereafter, Williams amended his petition in federal court, and the State filed a motion for summary judgment. The district court granted the State’s motion, denied Williams’s petition, and declined to grant a COA. Williams then filed a motion to alter the judgment pursuant to Federal Rule of Civil Procedure 59(e) based on the district court’s reliance on Ibarra v. Thaler, 687 F.3d 222 (5th Cir.2012), overruled by Trevino v. Thaler, — U.S. -, 133 S.Ct. 1911, 1921, 185 L.Ed.2d 1044 (2013), to reject his first claim as procedurally defaulted. The district court considered the motion in light of Trevino and concluded that the law had changed, but that the motion should nonetheless be denied. It *384then granted Williams a COA on his first claim only, and Williams timely appealed. He also sought to expand the COA to encompass two other rejected claims as to which the district court denied a COA. We address each in turn.
II. Discussion
A. Jurisdiction
The district court had jurisdiction over this case pursuant to 28 U.S.C. § 2254. Because the district court issued a COA on Williams’s first claim, we have jurisdiction to consider his appeal of this issue. 28 U.S.C. § 2253(c). Because the district court did not issue a COA on Williams’s other two claims asserted here, we have jurisdiction at this juncture only to consider whether a COA should issue on these claims. See id,.; Miller-El v. Cockrell, 537 U.S. 322, 335-36, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003).
B. Failure to Investigate and Present Social History Evidence
Williams argues that the district court erred in denying relief on his claim that trial counsel was ineffective for not conducting a thorough social history investigation and for not presenting additional social history evidence at the punishment phase of the trial. The district court found that this claim was procedurally defaulted because it was dismissed in state court as an abuse of the writ. Addressing the claim that Williams’s state habeas lawyer should have raised this issue in the original state habeas case, the district court held that Williams had failed to show that this issue had merit. Accordingly, even under Trevino, Williams had not shown cause and prejudice for the procedural default of the claim based on state habeas counsel’s failure to raise the claim.
Interestingly, after arguing repeatedly in the district court that the claim of “failure to investigate” was unexhausted and therefore procedurally defaulted, the State now attempts to argue on appeal that this claim was raised in the first state habeas proceeding, it is only the evidence in support of that claim that is new. Thus, the argument continues, consideration of the “new evidence” is barred by Cullen v. Pin-holster, where the Supreme Court held that “review under § 2254(d)(1) is limited to the record that was before the state court that adjudicated the claim on the merits.” — U.S. -, 131 S.Ct. 1388, 1398, 179 L.Ed.2d 557 (2011). Because it is not outcome determinative for Williams, we need not decide here where “the line” is between new evidence in support of a claim adjudicated on the merits in state court — which is barred from consideration by Pinholster — and a new claim — to which the Trevino equitable rule is argued as the only hope for avoiding a procedural default. See Pinholster, 131 S.Ct. at 1401 n. 10 (“[W]e do not decide where to draw the line between new claims and claims adjudicated on the merits....”); id. at 1418 n. 7 (Sotomayor, J., dissenting) (“The majority declines, however, to provide any guidance to the lower courts on how to distinguish claims adjudicated on the merits from new claims.”).
Examining the determination of the district court — that the “failure to investigate” claim was unexhausted and lacks merit — we agree with the district court. Under the doctrine of procedural default, “a federal court will not review the merits of claims, including constitutional claims, that a state court declined to hear because the prisoner failed to abide by a state procedural rule.” Martinez v. Ryan, — U.S. -, 132 S.Ct. 1309, 1316, 182 L.Ed.2d 272 (2012). The State argued below (and argues again on appeal in the alternative) that this doctrine applies to Williams’s first IAC claim because the *385CCA rejected the claim as an abuse of the writ. See Hughes v. Quarterman, 580 F.3d 336, 342 (5th Cir.2008). The district court agreed, and Williams does not take issue with this initial determination on appeal.
A petitioner may demonstrate cause and prejudice for failing to raise an IAC claim on initial state habeas review by showing: (1) that “appointed counsel in the initial-review collateral proceeding, where the claim should have been raised, was ineffective under the standards of Strickland,” and (2) that “the underlying ineffective-assistance-of-trial-counsel claim is a substantial one, which is to say that the prisoner must demonstrate that the claim has some merit.” Martinez, 132 S.Ct. at 1318; see Trevino, 133 S.Ct. at 1921 (holding that this doctrine applies when a petitioner fails to raise an IAC claim in an initial Texas state habeas proceeding). The district court approached this question by first determining that the underlying IAC claim was without merit and then finding, consequently, that the claim was insubstantial and that state — habeas counsel was not ineffective for failing to raise it. See Roberts v. Thaler, 681 F.3d 597, 605 (5th Cir.2012) (“While our normal procedure is to consider issues of procedural default first, we may nonetheless opt to examine the merits first....”). We agree with the district court that this IAC claim lacks merit such that Trevino offers no relief from the procedural default.
Williams’s argument centers on his counsel’s alleged failure to fully investigate and develop mitigation evidence in the form of information about his family, specifically, his father’s exposure to Agent Orange while serving in Vietnam. The Supreme Court has explained that a nonexistent or inadequate investigation cannot be justified,1 but counsel’s investigation does not have to uncover every conceivable fact to be reasonable:
[Strategic choices made after thorough investigation of law and facts relevant to plausible options are virtually unchallengeable; and strategic choices made after less than complete investigation are reasonable precisely to the extent that reasonable professional judgments support the limitations on investigation. In other words, counsel has a duty to make reasonable investigations or to make a reasonable decision that makes particular investigations unnecessary. In any ineffectiveness case, a particular decision not to investigate must be directly assessed for reasonableness in all the circumstances, applying a heavy measure of deference to counsel’s judgments.
Strickland v. Washington, 466 U.S. 668, 690-91, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). Here, trial counsel conducted an investigation, hired Cynthia Patterson to conduct a background and personal history investigation, and had Dr. Kessner conduct an investigation into Williams’s background and family history. Through these cumulative efforts, trial counsel uncovered the majority of the facts relied upon by Williams in this federal habeas case, including Williams’s father’s PTSD, Williams’s mother’s depression and attempted suicide, a number of family tragedies, and Williams’s extensive substance abuse.
The only allegedly important facts Williams claims were not discovered by trial counsel, but should have been, are that Williams’s father was exposed to *386Agent Orange and that Williams’s best friend died in his arms as a result of a drive-by shooting. Williams fails to demonstrate, however, that counsel acted unreasonably in the efforts made to conduct the relevant investigation. See Bobby v. Van Hook, 558 U.S. 4, 11, 130 S.Ct. 13, 175 L.Ed.2d 255 (2009) (“This is not a case in which the defendant’s attorneys failed to act while potentially powerful mitigating evidence stared them in the face.... ” (citation omitted)). Nor does it appear unreasonable for counsel to conclude that further investigation of Williams’s background was unnecessary in light of the information that was already discovered and the efforts he had made to obtain professional assistance in uncovering relevant facts. See id. (noting that there comes a point in which further investigation can be “expected to be only cumulative, and the search for it distractive from more important duties”); Rompilla, 545 U.S. at 389, 125 S.Ct. 2456 (“Questioning a few more family members and searching for old records can promise less than looking for a needle in a haystack, when a lawyer truly has reason to doubt there is any needle there.”). Further, while we recognize that deference to counsel’s strategic decisions does not excuse an inadequate investigation, see, e.g., Escamilla v. Stephens, 749 F.3d 380, 392-93 (5th Cir.2014), we conclude that the additional evidence does not significantly add to the discovered evidence such that failure to discover it would amount to ineffective assistance. Williams’s argument about the Agent Orange evidence (that his father’s exposure to it contributed to Williams propensity to commit this crime) is speculative at best, and family tragedies similar to Williams’s witnessing of his friend’s death were presented. Williams thus fails to satisfy his burden of showing “that counsel’s representation fell below an objective standard of reasonableness” due to a deficient investigation. Strickland, 466 U.S. at 688, 104 S.Ct. 2052.
Addressing counsel’s strategic decision not to offer additional social history evidence regarding Williams’s family difficulties that his investigation did uncover, Williams argues only that counsel “did not have enough information upon which to base” his strategic decision. As explained above, Williams fails to show that the investigation that was conducted was deficient. Thus, the corollary argument that the strategic decision was uninformed fails.
In any event, counsel’s strategy at the punishment phase was to “emphasize the numerous positive aspects of [Wiliams’s] life,” have Williams accept responsibility and express remorse for his actions, and avoid putting on evidence that could be perceived as Williams making excuses for his actions in order to show that he was not “a future danger and was a good person with a lifetime of good friends and family.” As the district court recognized, trial counsel’s reason for not presenting additional evidence of Williams’s family difficulties and tragedies of which counsel was aware is evident: it directly conflicted with counsel’s strategy at the punishment phase. See Pinholster, 131 S.Ct. at 1407 (explaining that a court is “required not simply to give [the] attorneys the benefit of the doubt, but to affirmatively entertain the range of possible reasons [the petitioner’s] counsel may have had for proceeding as they did” (citations and internal quotation marks omitted)).
Given the double-edged nature of this evidence and its ability to undermine counsel’s strategy at the punishment phase of the trial, Williams has failed to “overcome the presumption that, under the circumstances, the challenged action might be considered sound trial strategy.” Strickland, 466 U.S. at 689, 104 S.Ct. 2052 (cita*387tion and internal quotation marks omitted); see Brown v. Thaler, 684 F.3d 482, 499 (5th Cir.2012) (finding reasonable counsel’s decision to not offer evidence of a defendant’s troubled, impoverished, and disadvantaged background because the evidence was “double-edged” in that it “might suggest [that he], as a product of his environment, is likely to continue to be dangerous in the future” (citation and internal quotation marks omitted)). We thus conclude that the district court did not err in denying relief for this IAC claim.
C. Failure to Present Mitigating Evidence of Drug Use
For the same reason, we deny Williams’s application for a COA based upon his contention that, during the punishment phase, counsel should have presented mitigating evidence of Williams’s drug use. Specifically, Williams claims that trial counsel was ineffective for failing to present as mitigation evidence: (1) Williams’s extensive substance abuse history, including that Williams consumed drugs in conjunction -with the crime spree in question; and (2) expert testimony that without the drugs, it was highly unlikely that Williams would have engaged in the criminal behavior in question.
In order to obtain a COA to appeal the district court’s denial of this claim, Williams must make “a substantial showing of the denial of a constitutional right.” § 2253(c)(2). To meet this jurisdictional prerequisite, Williams must “sho[w] that reasonable jurists could debate whether (or, for that matter, agree that) the petition should have been resolved in a different manner or that the issues presented were adequate to deserve encouragement to proceed further.” See Miller-El, 537 U.S. at 336, 123 S.Ct. 1029 (citation and internal quotation marks omitted). In death penalty cases, this court resolves “any doubts as to whether a COA should issue” in the petitioner’s favor. Blue v. Thaler, 665 F.3d 647, 653 (5th Cir.2011) (citation and internal quotation marks omitted).
Where, as here, a petitioner’s claims were adjudicated on the merits in state court, we view “the petitioner’s arguments through the lens of the deferential scheme laid out in 28 U.S.C. § 2254(d).” Bar-rientes v. Johnson, 221 F.3d 741, 772 (5th Cir.2000); see also Miller-El, 537 U.S. at 340-41, 123 S.Ct. 1029. Under § 2254(d), Williams must demonstrate that the state court’s resolution of his claims (1) “was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States,” or (2) “was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.” § 2254(d). Stated differently, Williams ultimately “must show that the state court’s ruling on the claim[s] ... was so lacking in justification that there was an error well understood and comprehended in existing law beyond any possibility for fairminded disagreement.” Harrington v. Richter, 562 U.S. 86, 131 S.Ct. 770, 786-87, 178 L.Ed.2d 624 (2011). We address the request for a COA with these principles in mind.
The state habeas court (the findings of which were adopted by the CCA) found that, “as a matter of trial strategy to demonstrate that the applicant was not a future danger, trial counsel elected to emphasize the applicant’s positive aspects rather than the applicant’s alleged drug abuse,” and that this was a reasonable trial strategy. We conclude that “jurists of reason” would not find debatable the question of whether the state court made an unreasonable finding in concluding that failing to offer the substance abuse evidence was a reasonable trial strategy be*388cause it was “double edged” evidence that was just as likely to suggest to the jury that Williams would be a future danger. See Hopkins v. Cockrell, 325 F.3d 579, 586 (5th Cir.2003) (“As for the alcohol and drug abuse, this Court has repeatedly denied claims of ineffective assistance of counsel for failure to present ‘double edged’ evidence where counsel has made an informed decision not to present it.”); Boyle v. Johnson, 93 F.3d 180, 187-88 (5th Cir.1996). Accordingly, we deny a COA on this claim.
D. Exclusion of Dunn’s Statement
Turning to the second request for an expanded COA, Williams argues that the state court violated his Due Process and Eighth Amendment rights by excluding the evidence of his accomplice’s statement 2 in which, among other things, Dunn stated that he saw Carter hit Williams “like he was pushing him away or whatever,” and then Dunn “heard the gun go off.” The court excluded the statement because it was hearsay, cumulative, and “not crucially important to the determination of any of the issues at the punishment phase of trial.”
Williams claims that by excluding this statement, which implies that Carter’s shooting was accidental, at the punishment phase of his trial, the trial court violated his Due Process right to present his defense and his Eighth Amendment right to present relevant mitigation evidence. Specifically, Williams states in his federal ha-beas petition that he sought to admit this statement “in support of his contention that he did not intend to kill Matthew Carter,” so as to lead the jury away from the death penalty.
Addressing this argument on direct appeal, the CCA held, “To the extent appellant sought to use Dunn’s testimony to support the proposition that he did not intend to kill Carter, he sought to reliti-gate the issue of guilt, and he was not entitled to do so.” Williams, 273 S.W.3d at 231-32.3 The district court held that the CCA’s ruling was reasonable and recognized that Williams’s argument boils down to a question of intent, which was already litigated during the guilt-innocence phase.
We conclude that jurists of reason could not debate whether the CCA’s ruling was a reasonable application of controlling federal constitutional law as announced by the Supreme Court in light of Oregon v. Guzek, 546 U.S. 517, 126 S.Ct. 1226, 163 L.Ed.2d 1112 (2006). There, the Supreme Court addressed the same two-pronged argument made by Williams and explained that it has never held that a defendant has an Eighth Amendment or Due Process right to present new evidence at the punishment phase “designed to cast ‘residual doubt’ on his guilt of the basic crime of conviction.” Id. at 525, 126 S.Ct. 1226; see also Franklin v. Lynaugh, 487 U.S. 164, 174, 108 S.Ct. 2320, 101 L.Ed.2d 155 (1988) *389(plurality op. of White, J.); Holland v. Anderson, 583 F.3d 267, 278 (5th Cir.2009). Guzek directly applies here because Williams explained both at trial and in his federal habeas petition that he sought to introduce the new evidence of Dunn’s statement at the punishment phase “in support of his contention that he did not intend to kill Matthew Carter,” a question necessarily resolved against him in the guilt-innocence phase of the trial when he was found guilty of capital murder. See Holland, 583 F.3d at 278-79 (applying Guzek because (1) the evidence concerned whether, not how, the defendant committed the crime, and (2) the issue was actually litigated and decided against the defendant at the guilt-innocence phase). Thus, Williams has failed to show that reasonable jurists could debate whether the petition should have been resolved in a different manner. See Miller-El, 537 U.S. at 336, 123 S.Ct. 1029. We deny this request for a COA.
Accordingly, we AFFIRM the district court’s ruling regarding the IAC claim premised on a failure to investigate and present social history evidence and DENY the application for an expanded COA.
Pursuant to 5th Cir. R. 47.5, the court has determined that this opinion should not be published and is not precedent except under the limited circumstances set forth in 5th Cir. R. 47.5.4.
. Examples of cases addressing inadequate investigation include Rompilla v. Beard, 545 U.S. 374, 125 S.Ct. 2456, 162 L.Ed.2d 360 (2005), Wiggins v. Smith, 539 U.S. 510, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003), and Williams v. Taylor, 529 U.S. 362, 395, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000).
. The statement in question was one Dunn gave to police after the shooting. Dunn could not be called as a witness because his counsel notified the parties that Dunn would invoke his Fifth Amendment right not to testify. Williams, 273 S.W.3d at 231. At the guilt-innocence phase of the trial, counsel made the strategic decision not to offer Dunn’s statement once he leárned the prosecution would offer rebuttal evidence of Williams’s participation in the rest of the crime spree.
. The CCA also addressed the situation in which it assumed, alternatively, that the evidence was offered to "support the proposition that appellant’s decision to shoot was impulsive rather than premeditated.” Williams, 273 S.W.3d at 232. However, we need not address this alternative line of reasoning because Williams admits that he sought to introduce this statement to support the proposition that he did not intend to kill Carter.