ON PETITION FOR REHEARING
Treating the petition for rehearing en banc as a petition for panel rehearing, the petition for rehearing is GRANTED. We WITHDRAW our earlier opinion, Crutsinger v. Stephens, 540 Fed.Appx. 310 (5th Cir.2013), in its entirety, and SUBSTITUTE the following:
Petitioner-Appellant Billy Jack Crut-singer was convicted of capital murder and sentenced to death in Tarrant County, Texas. Crutsinger now requests a certificate of appealability (“COA”) to appeal the district court’s denial of his petition for federal habeas relief. For the following reasons, his request for a COA is DENIED.
Background
On April 6, 2003, Crutsinger fatally stabbed eighty-nine-year-old Pearl Mago-uirk and her seventy-one-year-old daughter, Patricia Syren. A Texas jury convicted him of capital murder, and, based on the jury’s answers to the special issues in the court’s charge, the trial judge sentenced him to death. The Texas Court of Criminal Appeals (“TCCA”) affirmed the conviction and sentence on direct appeal, and the U.S. Supreme Court denied Crutsinger’s petition for writ of certiorari. Crutsinger v. State, 206 S.W.3d 607, 608 (Tex.Crim.App.2006), cert. denied, 549 U.S. 1098, 127 S.Ct. 836, 166 L.Ed.2d 670 (2006).
While his direct appeal was pending, Crutsinger filed a state habeas corpus application, raising eighteen claims for relief. On November 7, 2005, the state trial judge issued findings of fact and conclusions of law recommending that relief be denied. Two years later, the TCCA adopted the trial judge’s findings and conclusions and denied relief. Ex parte Crutsinger, No. WR-63, 481-01, 2007 WL 3277524, at *1 (Tex.Crim.App. Nov. 7, 2007). Crutsinger then sought federal habeas relief, and new counsel was appointed to represent him in federal court.
On May 8, 2008, before filing his federal habeas petition, Crutsinger sought funding for investigative and expert assistance in the development of his claim that his trial counsel was ineffective in failing to timely initiate a social history investigation. The district court determined, however, that this specific ineffective-assistance-of-counsel (“LAC”) claim was procedurally barred from review. Crutsinger attempted to establish an exception to the exhaustion requirement under 28 U.S.C. § 2254(b)(1)(B)(ii) by arguing that circumstances existed that rendered the state corrective process ineffective to protect his rights. Specifically, Crutsinger claimed that “during the time that his state habeas application was pending, the general ineffectiveness of state habeas counsel appointed throughout Texas rendered the entire state habeas process ineffective to protect the rights of death-row habeas petitioners.” The court rejected this “innovative and far-reaching construction of th[e] statutory exception” and instead denied the pre-petition funding based on “an abundance of case law establishing that the ineffective assistance of state habeas *425counsel cannot justify a failure to comply with the exhaustion requirement or excuse any resulting procedural default.”
Crutsinger then filed a habeas petition under 28 U.S.C. § 2254, alleging three grounds for relief, including the IAC claim for which he had previously sought funding. Crutsinger alleged that (1) the trial court failed to suppress evidence resulting from his illegal arrest in violation of the Fourth Amendment, (2) his trial counsel provided ineffective assistance in failing to timely initiate a social history investigation, which caused counsel to overlook evidence of his mental impairments caused by alcohol addiction, head trauma, depression, and low intelligence, and (3) actual innocence. After determining that Stone v. Powell, 428 U.S. 465, 494, 96 S.Ct. 3087, 49 L.Ed.2d 1067 (1976), barred consideration of Crutsinger’s Fourth Amendment claim, the court addressed the IAC claim.
Though the court had found that the substance of the IAC claim was not developed in state court, the Government did |ot assert a procedural bar and instead argued the merits of the claim. Under these circumstances, the court declined to apply a procedural bar sua sponte and instead reviewed the claim de novo because “the record contain[ed] sufficient facts to make an informed decision on the merits.” The court determined that Crut-singer was unable to show either that his counsel’s performance fell below an objective standard of reasonableness or that he was prejudiced by counsel’s deficient performance. See Strickland v. Washington, 466 U.S. 668, 694, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). As a result, the court rejected Crutsinger’s IAC claim, and, finding his actual innocence claim to also lack merit, denied his habeas petition and denied COA.
Shortly thereafter, Crutsinger moved to alter the judgment under Federal Rule of Civil Procedure 59(e). After the district court denied that motion, Crutsinger initiated the present proceeding, requesting that this Court issue a COA.
Discussion
Under the Antiterrorism and Effective Death Penalty Act of 1996, petitioners may not appeal the denial of habeas relief without securing a COA. 28 U.S.C. § 2253(c)(1); Miller-El v. Cockrell, 537 U.S. 322, 335-36, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003). To obtain a COA, the petitioner must make “a substantial showing of the denial of a constitutional right.” 28 U.S.C. § 2253(c)(2). “A petitioner satisfies this standard by demonstrating that jurists of reason could disagree with the district court’s resolution of his constitutional claims or that jurists could conclude the issues presented are adequate to deserve encouragement to proceed further.” Miller-El, 537 U.S. at 327, 123 S.Ct. 1029.
On review, we must issue a COA if “reasonable jurists would find the district court’s assessment of the constitutional claims debatable or wrong.” Id. at 338, 123 S.Ct. 1029. “[A] claim can be debatable even though every jurist of reason might agree, after the COA has been granted and the case has received full consideration, that petitioner will not prevail.” Id. “This threshold inquiry does not require full consideration of the factual or legal bases adduced in support of the claims.” Id. at 336, 123 S.Ct. 1029. It requires only “an overview of the claims in the habeas petition and a general assessment of their merits.” Id. For death penalty cases, “any doubts as to whether the COA should issue are resolved in favor of the petitioner.” Moore v. Quarterman, 534 F.3d 454, 460 (5th Cir.2008).
Crutsinger requests a COA for his claim that his trial counsel provided ineffective assistance by failing to adequately investí-*426gate and develop evidence in all phases of the trial. Although Crutsinger presented an IAC claim in the state habeas proceeding based on trial counsels’ alleged failure to investigate generally, the district court determined that the federal iteration of Crutsinger’s IAC claim — one concerned with the timing of the investigation rather than the general failure to adequately conduct one — had not been developed in state court. The court nevertheless reviewed the claim de novo, declining to raise the procedural bar sua sponte. Our review, therefore, is limited to whether reasonable jurists would find debatable or wrong the district court’s determination of Crutsinger’s IAC claim.
A. IAC Claim
“The Sixth Amendment provides for the right to counsel, and the Supreme Court has recognized that ‘the right to counsel is the right to effective assistance of counsel.’ ” Neville v. Dretke, 423 F.3d 474, 482 (5th Cir.2005) (quoting Strickland, 466 U.S. at 686, 104 S.Ct. 2052). To establish a denial of that right, the petitioner must demonstrate (1) that counsel’s performance “fell below an objective standard of reasonableness,” and (2) that the deficient performance prejudiced the petitioner’s case. Strickland, 466 U.S. at 688-92, 104 S.Ct. 2052. Failure to satisfy either prong is fatal to an IAC claim.
In evaluating Strickland’s first prong, counsel’s performance is measured against an objective standard of reasonableness under prevailing professional norms. Rompilla v. Beard, 545 U.S. 374, 380, 125 S.Ct. 2456, 162 L.Ed.2d 360 (2005). Because there are countless ways to provide effective assistance, the petitioner must overcome “a strong presumption that counsel’s conduct falls within the wide range of reasonable professional assistance.” Strickland, 466 U.S. at 689, 104 S.Ct. 2052. “In judging the defense’s investigation, as in applying Strickland generally, hindsight is discounted by pegging adequacy to counsel’s perspective at the time investigative decisions are made and by giving a heavy measure of deference to counsel’s judgments.” Rompilla, 545 U.S. at 381, 125 S.Ct. 2456 (internal quotation marks and citations omitted).
During the underlying criminal proceedings, the trial court appointed, on counsel’s motion, a forensic psychologist, Dr. Kelly Goodness, as a mitigation specialist to investigate Crutsinger’s social history. In their affidavit to the state habeas court, Crutsinger’s trial counsel explained that Dr. Goodness’s evaluation would not have benefitted Crutsinger at punishment and that the use of her report would have allowed the State to present evidence based on its own expert’s evaluation. The district court determined that both this decision and the underlying investigation into Crutsinger’s social history were reasonable and that, even if counsel’s performance had been deficient, Crutsinger failed to establish that the performance prejudiced his case.
Rather than challenge the substance of the district court’s determination, Crut-singer now, as in his motion to alter the judgment, argues that the district court misconstrued his IAC claim and denied relief on a weaker claim that he never asserted. Specifically, he claims that his argument is that trial counsel should have investigated further into his mental health based on the “red flags” raised in Dr. Goodness’s report — not that trial counsel should have presented Dr. Goodness’s testimony at trial. He claims that only “after further investigation and sufficient development of evidence of brain impairment, and the psychosocial history of Mr. Crut-singer, could counsel then make an in*427formed decision on whether to present such evidence or not.”
Despite Crutsinger’s claim to the contrary, the district court addressed the arguments that he raised in his habeas petition. The essence of Crutsinger’s IAC claim was that trial counsel failed to timely investigate Crutsinger’s social history and, because the investigation was conducted too late, trial counsel lacked sufficient information to develop a viable strategy. For example, Crutsinger argued that a timely investigation would have revealed that one of the critical themes running throughout the case was his alcohol addiction, which, together with scientific information about the disease of alcohol addiction, would have provided a basis for trial counsel to (1) assert that Crutsinger’s confession was nonvoluntary, (2) negate mens rea, and (3) offer a credible response to the prosecution’s assertion that Crutsinger was “evil.” Similarly, Crutsinger argued that Dr. Goodness’s report revealed that he had several mental impairments and had suffered prior head trauma, both of which were factors that, had they been discovered earlier, could have been used to undercut the voluntariness of his confession and his criminal responsibility.
The district court rejected these specific arguments. First, the court determined that the investigation was timely and adequate. The court found that Crutsinger’s assumption that trial counsel did not consult Dr. Goodness until the day she issued her written report was contradicted by Dr. Goodness’s indication that she would first make an oral report to trial counsel and prepare a written report only if requested. Additionally, the court found that even if Crutsinger could show that trial counsel made strategic decisions without the benefit of Dr. Goodness’s investigation, he still could not establish prejudice. The court found no evidence, either in the record or in the materials Crutsinger submitted with his habeas petition, to support any of the defenses Crutsinger claimed he could have asserted.
It is only now in his application for COA that Crutsinger asserts that his true argument was that trial counsel should have investigated further upon learning of certain “red flags” in Dr. Goodness’s report. But even if this were the argument he presented in his habeas petition, the district court’s reasoning encompasses it. The critical issue in both of Crutsinger’s arguments is whether the investigation was reasonable, and the district court determined that it was. As the district court noted,
Counsel here hired a forensic psychologist who, with the assistance of a social worker and psychological associate, conducted a mitigation investigation that is documented in a twenty-three page report. That report is supported by interviews with Petitioner’s friends and family, document review summaries, a criminal history, fourteen hours of clinical interviews with Petitioner, and the administration of nineteen different psychological instruments.
We find no reason to dispute the district court’s determination that this investigation was reasonable. Indeed, Crutsinger himself does not challenge the thoroughness of Dr. Goodness’s report, relying instead on the red flags within it that should have alerted trial counsel of the need for further testing. Counsels’ decision to terminate the investigation, however, was made after a thorough investigation by Dr. Goodness, and “strategic choices made after thorough investigation of law and facts relevant to plausible options are virtually unchallengeable.” Strickland, 466 U.S. at 690, 104 S.Ct. 2052; see also Wiggins v. Smith, 539 U.S. 510, 533, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003) (“Strickland does *428not require counsel to investigate every conceivable line of mitigating evidence no matter how unlikely the effort would be to assist the defendant at sentencing.”).
We find that the evidence supports the district court’s determination that counsel conducted a thorough investigation. Based on that investigation, counsel made the strategic decision not to present Dr. Goodness’s testimony and not to pursue further investigation. Though Crutsinger now challenges the failure to pursue further investigation, he has not explained what the additional investigation he requests would reveal nor how it would have changed the result of his trial and sentence. Consequently, Crutsinger has failed to cast doubt on the district court’s conclusion that “[c]ounsels’ investigation in this case was not deficient, but was guided by sufficient information upon which a reasonable strategic decision could be made.” Under these circumstances, fairminded jurists could not disagree with the district court’s determination of Crutsinger’s IAC claim. We therefore deny Crutsinger’s application for COA.
B. Denial of Funding Under 18 U.S.C. § 3599
Crutsinger purports to challenge the district court’s denial of his application for investigative funding under 18 U.S.C. § 3599(f). But Crutsinger did not move to amend the underlying § 3599 application decision, nor did he include the denial of his funding application in his notice of appeal. Therefore, there is an initial question whether we have jurisdiction to review the district court’s denial of Crutsinger’s funding application.
Under Federal Rule of Appellate Procedure 3(c)(1)(B), a notice of appeal must “designate the judgment, order, or part thereof being appealed.” Fed. R.App. P. 3(c)(1)(B). In evaluating the notice of appeal, the general rule is that this court “has no jurisdiction to review any ... issues [that] are not expressly referred to and [that] are not impliedly intended for appeal.” Woodward v. Epps, 580 F.3d 318, 333 (5th Cir.2009) (internal quotation marks omitted). That said, “[a]n appeal from a final judgment preserves all prior orders intertwined with the final judgment.” N.Y. Life Ins. Co. v. Deshotel, 142 F.3d 873, 884 (5th Cir.1998) (internal quotation marks omitted).
In Woodward, we concluded that we had jurisdiction to review a denial of funding even though the petitioner had only sought appeal on his habeas petition. We reasoned that an appellate court’s consideration of a district court’s denial of funding to investigate an IAC claim “will often implicate the merits of a petitioner’s habeas claim.” 580 F.3d at 333 (citing Smith v. Dretke, 422 F.3d 269, 288 (5th Cir.2005)). “Even if there was a mistake in designating the judgment, a mistake in designating orders to be appealed should not bar review ‘if the intent to appeal a particular judgment can be fairly inferred, and if the appellee is not prejudiced or misled by the mistake.’ ” Id. at 333-34. Thus, in determining whether Crutsinger intended to appeal the district court’s decision denying funding, we not only examine his notice of appeal, but we may also consider his request for a COA in the district court and his opening appellate brief. See id. at 334. We also consider whether the state was prejudiced by the petitioner’s failure to designate the funding denial in his appeal. Id.
Here, Crutsinger could have appealed the denial of funding, but he did not. In his notice of appeal, Crutsinger indicated only that he was seeking appeal from the denial of his habeas petition and the denial of his motion to amend or alter judgment under Rule 59(e). Yet Crutsing*429er’s request for a COA and his accompanying brief clearly show an intent to appeal the denial. Crutsinger’s repeated reference to the funding denial and arguments for relief from that order have given the state notice and an opportunity to respond to those arguments. Therefore, we will review Crutsinger’s appeal of the denial of funding.1
Section 3599 provides that a district court may authorize a defendant’s attorneys to obtain investigative, expert, or other services upon a finding that such services “are reasonably necessary for the representation of the defendant.” 18 U.S.C. § 3599(f).2 If the court finds that such services are reasonably necessary, it “shall order the payment of fees and expenses therefor.” Id. Reasonably necessary in this context means “that a petitioner must demonstrate ‘a substantial need’ for the requested assistance.” Riley v. Dretke, 362 F.3d 302, 307 (5th Cir.2004) (quoting Clark v. Johnson, 202 F.3d 760, 768 (5th Cir.2000)). “A petitioner cannot show a substantial need when his claim is proeedurally barred from review.” Id. Similarly, the denial of funding will be upheld when it would only support a merit-less claim or when it would only supplement prior evidence. Woodward, 580 F.3d at 334. We review a district court’s denial of a § 3599 funding application for abuse of discretion. Id.
First, Crutsinger argues that the district court erred by refusing to raise sua sponte a procedural bar in reviewing his IAC claim in his habeas petition even though the court had four years earlier denied his application for funding because his claim was proeedurally defaulted. This discrepancy, he argues, means the court should have revisited its decision and granted him funding for investigative and expert assistance in the development of his IAC claim under 18 U.S.C. § 3599. Second, Crut-singer argues that the district court’s decision to deny funding was incorrect in light of an intervening change in law in Martinez v. Ryan, — U.S. -, 132 S.Ct. 1309, 182 L.Ed.2d 272 (2012).
We hold that the district court’s decision to address the merits of the claim does not establish an abuse of discretion for its first funding decision. The court relied on our well-established rule in denying funding to investigate a claim that would be proeedurally barred from review. See Riley, 362 F.3d at 307. It was only after Crutsinger applied for habeas relief and the State did not seek to apply the procedural bar that the court decided to reach the merits. The decision not to apply the procedural bar sua sponte was within the district court’s discretion. See 28 U.S.C. § 2254(b)(2) (“An application for a writ of habeas corpus may be denied on the merits, notwithstanding the failure of the applicant to exhaust the remedies available in the courts of the State.”); Magouirk v. Phillips, 144 F.3d 348, 360 (5th Cir.1998) (‘We conclude that a federal district court may, in the exercise of its judicial discretion, raise procedural default sua sponte.”). That decision, however, does *430not undercut the court’s justification for the initial denial of funds — the claim the court reviewed was still procedurally defaulted and raised for the first time on federal habeas review. Additionally, the court even implied that it was unnecessary to revisit its prior funding decision when it determined that “the record contained] sufficient facts to make an informed decision on the merits.” Crutsinger has presented no argument to contradict this point. He simply asserts that “[h]ad the funding request been granted, the petition would have been resolved in a different manner than it was.” This conclusory statement is insufficient to establish that the district court abused its discretion in denying Crutsinger’s funding request.
Crutsinger next argues that the district court’s decision to deny funding was incorrect in light of the intervening change in the controlling law. In Martinez, the Supreme Court held,
Where, under state law, claims of ineffective assistance of trial counsel must be raised in an initial-review collateral proceeding, a procedural default will not bar a federal habeas court from hearing a substantial claim of ineffective assistance at trial if, in the initial-review collateral proceeding, there was no counsel or counsel in that proceeding was ineffective.
132 S.Ct. at 1320. In 2013, the Supreme Court confirmed that Martinez applied to Texas prisoners who technically had the ability to bring their IAC claim on direct appeal of their conviction, but for all intents and purposes had to bring it in their first habeas petition. Trevino v. Thaler, — U.S. -, 133 S.Ct. 1911, 1921, 185 L.Ed.2d 1044 (2013). Crutsinger argues that after Martinez, the district court’s justification for the denial of funds — that the ineffective assistance of state habeas counsel could not excuse any procedural default — is no longer correct.
Even under Martinez, however, Crutsinger could not show cause to excuse his procedural default. Under Martinez, Crutsinger has to establish that his underlying IAC claim is “substantial” and that his state habeas counsel was ineffective. 132 S.Ct. at 1318-19. He has not met the first of these requirements for overcoming the procedural default: Crutsinger has failed to show that his underlying IAC claim is substantial-that is, that it has “some merit.” Id. at 1318. Martinez makes this substantiality standard equivalent to the standard for obtaining a COA. Id. at 1318-19 (citing Miller-El v. Cockrell, 537 U.S. 322, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003) (describing the standard for granting a COA)); see also Detrich v. Ryan, 740 F.3d 1237, 1245 (9th Cir.2013) (en banc) (noting that “the [Martinez ] Court incorporated [the COA standard] in its definition of substantiality”); cf. Cook v. Ryan, 688 F.3d 598, 610 n. 13 (9th Cir.) (noting that Martinez referenced Miller-El as “generally analogous support”), cert. denied, — U.S. -, 133 S.Ct. 81, 183 L.Ed.2d 721 (2012). So, if a petitioner’s IAC claim is not substantial enough to earn a COA, it is also not substantial enough to form the basis for excusing the procedural default. Here, since we have already denied the COA on Crut-singer’s IAC claim because his claim was not “substantial,” Crutsinger has also failed to satisfy the Martinez substantiality requirement. Therefore, remand is not necessary, and we conclude that the district court did not abuse its discretion in denying Crutsinger’s funding application even after Martinez.3
*431Finally, Crutsinger makes a far-reaching argument that Martinez “obligated the district court to provide pre-petition funding” because it “tacitly acknowledges that litigating IAC claims requires not merely an effective attorney, but also one that had adequate resources to demonstrate the underlying claim is a substantial one in order to overcome procedural default.” Martinez, however, does not mandate pre-petition funding, nor does it alter our rule that a prisoner cannot show a substantial need for funds when his claim is procedurally barred from review. It provides only that “[i]nadequate assistance of counsel at initial-review collateral proceedings may establish cause for a prisoner’s procedural default of a claim of ineffective assistance at trial.” Martinez, 132 S.Ct. at 1315. Without both a showing under Strickland that state habeas counsel was ineffective and a demonstration that the underlying IAC claim “has some merit,” id. at 1318, Martinez offers no relief from a potential procedural default. Because Crutsinger has failed to show that his claim was substantial, Martinez does not provide excuse for Crutsinger’s procedural default.
Therefore, the district court did not abuse its discretion.
Conclusion
For the foregoing reasons, we AFFIRM the district court’s denial of Crutsinger’s § 3599 funding application. Additionally, because reasonable jurists could not disagree with the district court’s determination of Crutsinger’s IAC claim, Crutsinger’s request for a COA is DENIED.