JERRY E. SMITH, Circuit Judge:
Randall Mays was convicted of murder and sentenced to death. He seeks a certificate of appealability (“COA”) to challenge the constitutionality of the sentence. Because he has failed to make a substantial showing of the denial of a constitutional right, we deny a COA.
I.
In 2007, police officers responded to a “domestic violence-gunshot” call. All of them were in uniform, wearing badges, and driving marked vehicles. Although Mays was initially calm and courteous, he fled into his house and barricaded himself when the officers began reading him his rights. He later emerged holding a deer rifle. After the officers had failed several times to convince Mays to put down the weapon and give himself up, he opened fire. He shot Deputy Tony Ogburn and Officer Paul Habelt in the head, killing both, and shot Deputy Kevin Harris in the leg.
At the guilt phase of the trial, the defense produced evidence that Mays suffered from paranoia and mental illness but was not insane. The jury found Mays guilty of capital murder. During the sentencing phase, the prosecution provided victim-impact evidence from Harris and from Ogburn’s widow and son. The defense submitted mitigating evidence of Mays’s violent and abusive childhood and testimony from psychiatrists that he suffered from depression and a “psychotic disorder not otherwise specified,” which was possibly linked to permanent brain damage from his chronic methamphetamine use. The jury answered “yes” to the future dangerousness issue and “no” to the question of mitigation; the court sentenced Mays to death.
On direct appeal, the Texas Court of Criminal Appeals unanimously affirmed the conviction and sentence.
In state ha-beas corpus proceedings, the trial court,
after a live evidentiary hearing, recommended denial of relief. The Court of Criminal Appeals adopted the trial court’s findings of fact and conclusions of law and denied relief.
Mays filed a federal habeas petition raising nine issues. The magistrate judge recommended the petition be denied on all grounds, and the district court adopted the recommendation and denied the petition and a COA. Mays applies for a COA on four grounds: (1) constitutionally ineffective assistance of counsel (“IAC”) in failing to investigate mitigating evidence of severe mental illness; (2) constitutionally IAC in failing to request a competency hearing; (3) IAC in failing adequately to investigate and present evidence that he suffers from an intellectual disability and is thus ineligible to receive the death penalty, and the execution of Mays — as an individual with an intellectual disability— would violate the Eighth Amendment as cruel and unusual punishment; and (4) violation of the Eighth Amendment’s proscription of cruel and unusual punishment by imposing the death penalty on a defendant who is mentally ill.
II.
We may issue a COA only where a petitioner has made a “substantial showing of the denial of a constitutional right.” 28 U.S.C. § 2253(c)(2);
Miller-El v. Cockrell,
537 U.S. 322, 336, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003). He “must show that reasonable jurists could debate whether ... the petition should have been resolved in a different manner or that the issues presented were adequate to deserve encouragement to proceed further.”
Miller-El,
537 U.S. at 336, 123 S.Ct. 1029 (internal quotation marks and alteration omitted).
In making this determination, we must look to the district court’s application of the Antiterrorism and Effective Death Penalty Act of 1996 (“AEDPA”) to the petitioner’s claims and “ask whether that resolution was debatable amongst jurists of reason.”
Id.
This does not require a showing that the appeal will succeed or a “full consideration of the factual or legal bases adduced in support of the claims.”
Id.
at 336-37, 123 S.Ct. 1029. Instead, the debatability of AEDPA’s application to the underlying constitutional claims is determined merely on “an overview of the claims in the habeas petition and a general assessment of their merits.”
Id.
at 336, 342,123 S.Ct. 1029.
Under AEDPA, a federal court may not issue a writ of habeas corpus for a state conviction unless the adjudication of the claim
(1) 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; or
(2) resulted in a decision that was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceedings.
28 U.S.C. § 2254(d).
A state court’s decision is ‘contrary to’ clearly established federal law if (1) the state court ‘applies a rule that contradicts the governing law’ announced in Supreme Court cases, or (2) the state court decides a case differently than the Supreme Court did on a set of materially indistinguishable facts. [
]
“A state court’s application of clearly established federal law is ‘unreasonable’ within the meaning of AEDPA when the state court identifies the correct governing legal principle from Supreme Court precedent, but applies that principle to the case in an objectively unreasonable manner.”
“It is settled that a federal habeas court may overturn a state court’s application of federal law only if it is so erroneous that ‘there is no possibility fairminded jurists could disagree that the state court’s decision conflicts with this Court’s precedents.’ ”
When considering whether a decision is “based on an unreasonable determination of the facts in light of the evidence,” AED-PA provides that the “determination of a factual issue made by a State court shall be presumed to be correct” unless the applicant carries “the burden of rebutting the presumption of correctness by clear and convincing evidence.”
This presumption, however, applies not only to explicit findings of fact but “also ... to those unarticulated findings which are necessary to the state court’s conclusions of mixed law and fact.”
Valdez v. Cockrell,
274 F.3d 941, 948 n. 11 (5th Cir.2001). “The presumption is especially strong when the state habeas court and the trial court are one in the same,” as here.
Clark v. Johnson,
202 F.3d 760, 764 (5th Cir.2000).
III.
Mays presents two theories for relief regarding IAC. Because no reasonable jurist can debate that the state habeas court did not unreasonably apply controlling Supreme Court precedent in denying Mays’s IAC claims, we deny a COA as to those grounds.
Under
Strickland v. Washington,
466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), a claim of IAC has two components: “First, the defendant must show that counsel’s performance was deficient. This requires showing that counsel made errors so serious that counsel was not functioning as the ‘counsel’ guaranteed the defendant by the Sixth Amendment.”
Id.
at 687, 104 S.Ct. 2052. The proper measure of the attorney’s performance under this prong “remains simply reasonableness under prevailing professional norms.”
Id.
at 688, 104 S.Ct. 2052. A reviewing court, however, “must indulge a strong presumption that counsel’s conduct falls within the wide range of reasonable professional assistance” and that “under the circumstances, the challenged action might be considered sound trial strategy.”
Id.
at 689, 104 S.Ct. 2052 (internal quotation marks omitted).
“Second, the defendant must show that the deficient performance prejudiced the
defense. This requires showing that counsel’s errors were so serious as to deprive the defendant of a fair trial, a trial whose result is reliable.”
Id.
at 687, 104 S.Ct. 2052. In other words, “[t]he defendant must show that there is a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different. A reasonable probability is a probability sufficient to undermine confidence in the outcome.”
Id.
at 694,104 S.Ct. 2052.
In addition, because we are reviewing the determinations of a state habeas court, the deferential standard accorded to counsel’s representation under
Washington
must be considered “in tandem” with the deference accorded state court decisions under 28 U.S.C. § 2254(d).
Richter,
131 S.Ct. at 788. Because each standard alone is “highly deferential,” “when the two apply in tandem, review is doubly so.”
Id.
(internal quotation marks omitted). Under this double layer of discretion, “the question is not whether counsel’s actions were reasonable. The question is whether there is any reasonable argument that counsel satisfied
[Washington’s]
deferential standard.”
Id.
“If the standard is difficult to meet, that is because it was meant to be.”
Id.
at 786.
If the petitioner fails to satisfy either component, the IAC claim fails. “[TJhere is no reason for a court deciding an [IAC] claim to approach the inquiry in the same order or even to address both components of the inquiry if the defendant makes an insufficient showing on one.”
Washington,
466 U.S. at 697, 104 S.Ct. 2052. “If it is easier to dispose of an ineffectiveness claim on the ground of lack of sufficient prejudice, which we expect will often be so, that course should be followed.”
Id.
A.
Mays claims his counsel were constitutionally ineffective during the sentencing phase for failing to investigate the mitigating effects of his mental illness. More specifically, he reasons, counsel failed timely to investigate whether he had “organic brain damage” and therefore did not obtain the proper neuropsychological examination. As a result, that mitigation evidence was not produced at sentencing, arguably prejudicing Mays.
Although Mays’s counsel did not discover the jail record reflecting “organic brain damage” until after jury selection had commenced, once their investigator related this information to them counsel immediately hired a psychologist to pursue the lead. The state habeas court found that the psychologist and counsel made at least three attempts to conduct the necessary testing on Mays but that they were unable to convince Mays to cooperate. Instead, counsel introduced mitigating evidence in the form of expert testimony of “chronic and severe psychiatric illness” and methamphetamine abuse that is known to damage nerve cells and cause persisting psychosis. After sentencing, state habeas counsel was able to secure Mays’s cooperation for the additional examination, which indicated some organic brain damage.
Even assuming that Mays’s counsel was constitutionally deficient, there is a reasonable argument that Mays was not prejudiced. First, Mays has not shown that if trial counsel had had more time for examination before the sentencing phase, they would have successfully obtained Mays’s cooperation. Although it is true that habeas counsel was able to elicit the needed cooperation after sentencing, Mays’s willingness to submit to examination after having been sentenced to death provides little evidence of his potential willingness to do so before trial. Because it is reasonable to conclude that Mays would have declined to cooperate before
trial as he thrice declined after trial began, he failed to show prejudice under
Washington
or
Richter.
Second, even if earlier investigation into this “lead” had resulted in cooperation, examination, and the presentation of this evidence during the sentencing phase, Mays has failed to show a reasonable probability that, barring such hypothetical error, the result of the proceeding would have been different.
The state court found that the testimony provided by the additional examination was largely cumulative of the evidence of mental illness actually presented at trial; it added little or no weight to the mitigating evidence presented. Mays has not shown that decision to be based on an unreasonable determination of the facts in light of the evidence presented in the state court proceedings as required by 28 U.S.C. § 2254(d)(2) and, as a result, he has failed to show an unreasonable application of
Washington
under § 2254(d)(1).
There can be no dispute among reasonable jurists regarding prejudice. There is no need to consider whether counsel was constitutionally deficient, and the COA is denied as to this ground.
B.
Mays claims counsel were constitutionally ineffective for failing to request a competency hearing. Assuming that this was constitutional IAC, again Mays cannot establish prejudice. As the state court— which served as both state trial and habeas court — found, Mays presented no evidence that he was actually incompetent to stand trial: No testimony was introduced at the five evidentiary hearing that he was incompetent. Even the psychiatrist who testified regarding Mays’s organic brain chemistry did not testify as to his incompetency.
Instead, Mays merely points to the evidence presented regarding his mental illness to suggest incompetency during trial. Without more, however, such evidence says nothing about whether Mays had “sufficient present ability to consult with his lawyer with a reasonable degree of rational understanding — and whether he has a rational as well as factual understanding of the proceedings against him.”
Dusky v. United States,
362 U.S. 402, 402, 80 S.Ct. 788, 4 L.Ed.2d 824 (1960) (per curiam). The two are not coextensive: A defendant can be both mentally ill and competent to stand trial.
As a result, Mays failed to establish that the state court decision was based on an unreasonable determination of the facts in light of the evidence presented in the state proceedings or that its decision was an unreasonable application of
Washington
under § 2254(d). Without this, Mays also has not shown that there is a reasonable probability that, but for counsel’s failure to seek an incompetency hearing, the result of the proceeding would have been different and Mays would have been found incompetent to stand trial.
He cannot establish that reasonable jurists could debate this conclusion by the state court. Because Mays has not shown prejudice, there
is no need to consider whether counsel was constitutionally deficient, and the COA is denied as to this ground.
IV.
Mays initially sought habeas relief contending that his execution, “as an individual with an intellectual disability, would violate the Eighth Amendment’s prohibition against cruel and unusual punishment.” Because this claim was unexhausted, however, Mays reframed it in supplemental pleadings to include a claim of IAC by habeas counsel and claimed cause and prejudice for his procedural default under
Trevino v. Thaler,
— U.S. -, 133 S.Ct. 1911, 185 L.Ed.2d 1044 (2013). Nonetheless, the district court found that he did not satisfy the cause-and-prejudice standard and that this ground was proeedurally defaulted.
Because the court denied relief on procedural grounds, we issue a COA only if the petitioner shows
that jurists of reason would find it debatable whether the petition states a valid claim of the denial of a constitutional right and that jurists of reason would find it debatable whether the district court was correct in its procedural ruling.
Slack v. McDaniel,
529 U.S. 473, 484, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000). “Section 2253 mandates that both showings be made before the court of appeals may entertain the appeal ..., and a court may find that it can dispose of the application in a fair and prompt manner if it proceeds first to resolve the issue whose answer is more apparent from the record and arguments.”
Id.
at 485, 120 S.Ct. 1595. Because a reasonable jurist could not find the merits of Mays’s constitutional claim debatable,
we deny a COA on this ground.
Mays contends that the test established for mental retardation
in
Ex parte Brise-no,
135 S.W.3d 1, 5-9 (Tex.Crim.App.2004), is unconstitutional and that under the proper, constitutional definition he is mentally retarded. In
Briseno,
Texas adopted the three-pronged definition of the American Association on Mental Retardation (“AAMR”): (1) significantly subaverage general intellectual functioning; (2) accompanied by related limitations in adaptive functioning; (3) the onset of which occurs before age eighteen.
Id.
at 7. But, recognizing that the adaptive-behavior element is highly subjective, the court introduced seven “evidentiary factors” — commonly referred to as
Briseno
factors — for factfin-ders to consider in their determination of mental retardation.
Id.
at 8-9.
Mays posits that the application of these non-AAMR characteristics is an unconstitutional application of
Atkins.
Although we have upheld the use of the
Briseno
factors as a reasonable application of
Atkins,
Mays maintains that
Hall
casts doubt on the constitutionality of their continued use. We roundly disagree.
Contrary to Mays's assertions,
Hall
does not address the constitutionality of considering additional “non-diagnostic” factors in deciding mental retardation, nor does it require a wholesale adoption, without deviation, of AAMR or other professional standards and definitions. Instead, it exclusively addresses the constitutionality of mandatory, strict IQ test cutoffs.
In finding such mandatory cutoffs unconstitutional, the Court focused largely on the prohibition of sentencing courts’ considering even substantial, additional evidence of retardation — including poor adaptive functioning — for defendants who do not have an IQ score below 70.
Because this cutoff did not take into account the well-known imprecision of IQ testing, the Court was wary of any blanket restriction on a defendant’s ability to present further evidence of his disability.
The Court therefore held that sentencing courts must take into account IQ tests’ standard error of measurement (“SEM”) when assessing mental retardation.
Hall
therefore in no way affects this court’s reading and application of Briseno, and we so hold. First,
Hall
does not implieate Texas. Although the Court listed the states that could be affected by its ruling,
the word “Texas” nowhere appears in the opinion, and the reason is obvious: Texas has never adopted the bright-line cutoff at issue in
Hall. See, e.g., Hearn v. Thaler,
669 F.3d 265, 268-70 (5th Cir.2012).
Second, no reasonable jurist could theorize that the reasoning animating
Hall
could possibly be extended to
Briseno.
The cutoff at issue in
Hall
was problematic largely because it restricted the evidence — especially regarding adaptive functioning — that could be presented to establish intellectual disability. There is no similar restriction of evidence under
Brise-no.
To the contrary, the
Briseno
factors merely provide further guidance to sentencing courts as to
what kinds
of evidence the court might consider when determining adaptive functioning.
In other words,
Hall
did nothing to overturn or question
Atkins:
Even after
Hall,
states retain “the task of developing appropriate ways to enforce the constitutional restriction upon their execution of sentences”
and also retain “a critical role
in advancing protections and providing the Court with information that contributes to an understanding of how intellectual disability should be measured and assessed.”
Hall
merely states that that discretion is not “unfettered”: States cannot contravene the Court’s discussion of mental retardation in
Atkins.
Unlike the cutoff at issue in
Hall,
the
Briseno
factors do not conflict with
Atkins.
Although the
Atkins
Court cited definitions of mental Delaware, Kansas, North Carolina, and Washington. “Thus, at most nine States mandate a strict IQ score cutoff at 70.”
Id.
at 1997. retardation that expressly rejected the cutoff at issue in
Hall,
Atkins
says nothing about what kind of evidence should be considered when determining whether a defendant’s significantly subaverage general intellectual functioning meaningfully limits his adaptive functioning.
That question has been left explicitly to the states, and the definition adopted by Texas in
Briseno,
including the
Briseno
factors, in no way departs from any of the Court’s pronouncements.
Therefore, because Mays has made no attempt to present any evidence of limited adaptive functioning under
Briseno,
he has failed to provide evidence of mental retardation under Texas law and, as a result, has failed to show prejudice in urging his IAC claim. The motion for a COA is denied as to that ground.
V.
Mays seeks a COA on the ground that the Eighth Amendment prohibits his execution because he is mentally ill.
Fifth Circuit precedent, however, forecloses that. In
Neville,
440 F.3d at 221, we denied habeas relief, holding that neither
Atkins
nor
Roper v. Simmons,
543 U.S. 551, 125 S.Ct. 1183, 161 L.Ed.2d 1 (2005), created a rule of constitutional law making the execution of mentally ill persons unconstitutional.
Mays points to no subsequent Supreme Court decision announcing such a rule. Therefore, Mays has failed to show the state court’s decision to be “contrary to, or involv[ing] an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States.”
As a result, the request for a COA is denied as to this ground.
The application for a COA is in all respects DENIED.