Robert Carter appeals the denial of his petition for a writ of habeas corpus filed under 28 U.S.C. § 2254 (1996). We affirm the judgment and vacate the stay of execution.

Carter was convicted of capital murder and sentenced to death in March 1982. His case, which languished in the Texas courts for over a decade and recently reached the Supreme Court, has now been remanded to this court for further action.

Carter was arrested in 1981 and charged with the murder of Sylvia Reyes, who was fatally wounded during the robbery of a service station.1 Carter confessed in great detail to the murder but stated that the shooting had been accidental and denied any intent to kill Reyes. Pursuant to this confession, the police obtained the murder weapon identified by Carter, and ballistic experts confirmed that the revolver had been used in the murder.

At trial, a witness identified as "David Josa" testified that he was entering the service station when he heard gunshots inside and observed two individuals leave it immediately thereafter. The first fled but returned when the police arrived. The second, a young black man fitting Carter's description, emerged from the store with "a wad of money" in his left hand and fled. Josa observed this person for only a few seconds but did not see a gun, nor was he able subsequently to identify Carter as the second man.

Another witness, Arthur Mallard, corroborated Josa's testimony. Mallard identified himself as the first person out of the station and testified that he had observed a man fitting Carter's description reach across the counter to take money from the cash register. When the station attendant resisted, Mallard heard a gunshot and fled the store. He was unable to identify Carter as the man he had seen.

The defense offered no evidence to rebut the state, and the jury returned a verdict of guilty to capital murder. At the penalty stage, the state called witnesses to establish that Carter had committed another murder six days prior to the charged offense. Although none of the witnesses directly observed the second murder, one identified Carter as the man she observed fleeing the scene. Finally, the state introduced Carter's confession, in which he confessed to the second murder, once again.

In rebuttal, defense counsel offered the testimony of three witnesses--Carter, his mother, and a family friend--to establish Carter's good character. Carter testified that he had not intentionally killed the two victims and pledged to rehabilitate himself if sentenced to life imprisonment rather than death. Finally, in response to the character evidence, detective L.B. Smith testified that Carter's reputation as a peaceful and law-abiding citizen was "bad." After brief deliberation, the jury affirmatively answered the three special issues submitted pursuant to TEX.CODE CRIM.PROC.ANN. art. 37.071 (Vernon 1981), and the trial court imposed the death sentence.

In 1990, Carter filed his first state habeas petition. In August 1995, the state trial court recommended that state habeas relief be denied, and the Texas Court of Criminal Appeals denied this first habeas petition in December 1995.

In August 1995, while the original state habeas petition was pending, Carter filed his second state habeas application, alleging that the length of time between his sentencing and his scheduled execution rendered his death sentence cruel and unusual punishment in violation of the Eighth Amendment. The state trial court recommended that habeas relief be denied, and the Court of Criminal Appeals denied this second application in January 1996.

Having finally exhausted his state remedies, Carter filed the instant federal habeas petition in January 1996, followed soon thereafter by a motion for discovery, a motion for an evidentiary hearing, and an application for stay of execution. On March 20, 1996, the federal district court entered final judgment, denying habeas relief. Carter appealed, and the district court issued a certificate of probable cause ("CPC") on April 19, 1996.

We affirmed on April 9, 1997. See Carter v. Johnson, 110 F.3d 1098 (5th Cir.1997). On June 23, 1997, the Supreme Court decided Lindh v. Murphy, 521 U.S. ----, 117 S. Ct. 2059, 138 L. Ed. 2d 481 (1997). Carter then petitioned for writ of certiorari, raising, as his sole issue, whether the Supreme Court, "under its customary 'GVR' practice,2 should remand this case for further proceedings in light of Lindh v. Murphy...." (Citation omitted.) The Court in fact did so, vacating and remanding "for further proceedings in light of Lindh...." (Citation omitted.) See Carter v. Johnson, --- U.S. ----, 118 S. Ct. 409, 139 L. Ed. 2d 313 (1997).

Our initial opinion, 110 F.3d at 1103, involved an interpretation of the Antiterrorism and Effective Death Penalty Act ("AEDPA") of 1996, Pub.L. No. 104-132, 110 Stat. 1214 (1996),3 that has since been rejected by the Supreme Court. In Lindh, the Court rejected the argument that the procedural rules established in chapter 153 of the AEDPA, 28 U.S.C.A. § 2254(d) (1997), could be applied to cases initiated before the AEDPA's effective date. See Lindh, 521 U.S. at ----, 117 S. Ct. at 2068.

In our initial opinion, we held that the AEDPA's procedural provisions could be applied to Carter's habeas petition despite the fact that his case was initiated before the effective date. Carter, 110 F.3d at 1103. On the basis of this holding, we applied a highly deferential standard of review to the state and district habeas courts' conclusions regarding questions of law and mixed questions of law and fact. We assume that the Supreme Court remanded so that we may apply the correct standard of review to Carter's appeal.

Before reaching the merits, we must decide whether we have jurisdiction to entertain the appeal. Although neither party has challenged our jurisdiction, we are obliged to raise the issue sua sponte.4

The AEDPA became effective April 24, 1996, five days after Carter's CPC was issued. Under similar circumstances, we recently held that the AEDPA's requirement of a COA does not apply to habeas applicants who obtained CPC's prior to the statute's effective date. See Brown v. Cain, 104 F.3d 744, 749 (5th Cir.1997). Accordingly, we have jurisdiction.

When we initially decided this case, we followed Drinkard v. Johnson, 97 F.3d 751, 764-66 (5th Cir.1996), cert. denied, --- U.S. ----, 117 S. Ct. 1114, 137 L. Ed. 2d 315 (1997), and held that the amended standards of review established in § 104(3) the AEDPA (codified at 28 U.S.C. § 2254(d) (1997)) are procedural in nature and therefore apply immediately to all habeas petitions pending on the effective date of the AEDPA. See Carter, 110 F.3d at 1103. Under Lindh, however, this was error, and § 104(3) of the AEDPA does not apply to this case. Accordingly, we must take a fresh look at Carter's appeal, applying traditional standards of review to the district court's conclusions of law and applications of law to fact.5

Carter alleges that the state introduced the fraudulent testimony of an "imposter witness" at trial, thereby incriminating him and undermining the integrity of the verdict. To succeed on such a claim, Carter must establish three elements: first, that false testimony was presented at trial; second, that the prosecution had actual knowledge that the testimony was false; and third, that the testimony was material. May v. Collins, 955 F.2d 299, 315 (5th Cir.1992). Carter cannot satisfy this standard.

The sole evidence Carter offers to establish the first element is the affidavit of David Josza. Josza, who was identified as an eyewitness during the murder investigation, avers that he did not testify at Carter's trial. Nevertheless, the trial transcript indicates that an individual identified as "David Josa" testified for the prosecution, offering substantially the same testimony as the statement given by Josza during the investigation. Therefore, Carter concludes that the witness who testified at trial must have been an imposter. Even if we assume, arguendo, that the testimony was fraudulent, the introduction of fraudulent testimony is insufficient by itself to entitle Carter to habeas relief.6

The Fourteenth Amendment is implicated by the introduction of fraudulent or perjured testimony only if the prosecution has actual knowledge of the perjury.7 We have consistently stated that this requirement imposes a strict burden of proof on a federal habeas petitioner. See, e.g., May, 955 F.2d at 315; Koch v. Puckett, 907 F.2d 524, 531 (5th Cir.1990). Carter cannot satisfy this burden.

Carter relies exclusively on circumstance and inference, arguing that an "imposter witness" could not possibly testify at trial without the substantial complicity of the prosecution. To rebut this inference, the state introduced the affidavit of then-prosecutor Brian Rains, which the state court found to be credible, averring that he would not knowingly or intentionally present an imposter witness at trial. After weighing this competing evidence, the state court concluded there was no evidence that the state had knowingly or intentionally presented an "imposter witness" at trial.

These factual findings are entitled to a presumption of correctness.8 The state court reasonably determined that Carter had not satisfied his burden to prove that the prosecution knowingly or intentionally presented perjured testimony at trial. We have no reason to doubt either the fairness of the state court's procedure or the correctness of its result.C.

Both the state habeas court and the federal district court dismissed the perjury claim on the ground that the alleged perjury was not material to the outcome of the trial. For the perjury to be material, Carter must show that "there was any reasonable likelihood that the false testimony could have affected the judgment of the jury."9 Under the circumstances of this case, Carter cannot make such a showing.

Given that the star witness for the prosecution was Carter, whose confession was introduced into evidence, there is no reasonable likelihood that Josa's allegedly false testimony affected the verdict. The prosecution did not rely on Josa's testimony to establish the essential elements of the offense, but merely to corroborate the confession. Moreover, the contested evidence was cumulative of other evidence, particularly Mallard's testimony.

Carter has failed to establish that the prosecution knowingly and intentionally presented material false evidence. Accordingly, we find no error in the state court's determination on this issue.

Carter contends that the district court erred by failing to conduct a nunc pro tunc evidentiary hearing to determine his competency to stand trial. We disagree.

The trial and conviction of a defendant while he is mentally incompetent constitute a denial of due process. See Cooper v. Oklahoma, 517 U.S. 348, ----, 116 S. Ct. 1373, 1376, 134 L. Ed. 2d 498 (1996). The constitutional standard for competency to stand trial is whether the defendant "has sufficient present ability to consult with his lawyer with a reasonable degree of rational understanding--and whether he has a rational as well as a 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); accord Godinez v. Moran, 509 U.S. 389, 396, 113 S. Ct. 2680, 2685, 125 L. Ed. 2d 321 (1993). Carter claims that he adduced sufficient evidence in the state courts to warrant a federal nunc pro tunc evidentiary hearing on the question of whether he was incompetent in fact.10

A habeas petitioner is entitled to a nunc pro tunc evidentiary hearing for the purpose of proving that he was incompetent at the time of trial only "when he makes a showing by clear and convincing evidence to raise threshold doubt about his competency." Lokos v. Capps, 625 F.2d 1258, 1261 (5th Cir.1980). In order for him to raise such doubt, he must present facts sufficient "to positively, unequivocally and clearly generate a real, substantial and legitimate doubt" concerning his mental capacity.11 "When federal habeas is sought on the ground that the defendant was in fact incompetent at the time of trial, the petitioner's initial burden is substantial." Enriquez v. Procunier, 752 F.2d 111, 114 (5th Cir.1984).

Both the state habeas court and the federal district court concluded that a nunc pro tunc evidentiary hearing was not required to decide whether Carter was incompetent at trial. Indeed, the state habeas court expressly concluded that Carter was competent: "The Court finds that the applicant's testimony during the punishment stage of the trial shows a factual, as well as rational understanding of the proceedings against him." Moreover, the state habeas court entered the following conclusion: "The applicant fails to show that he was legally incompetent to stand trial, i.e., that he was unable to consult with counsel with a reasonable degree of rational understanding or that he lacked a factual, as well as rational, understanding of the proceedings against him." These findings are more than adequate to justify the district court's conclusion that "the state court found that there was no evidence that Petitioner was actually incompetent to stand trial."12

Under 28 U.S.C. § 2254(d), the findings are entitled to a presumption of correctness. The petitioner must rebut this presumption by clear and convincing evidence, and a federal court may not issue a writ unless the petitioner can demonstrate by such evidence that the state decision was based on an incorrect determination of the facts. Furthermore, the factual determination of the state habeas court, finding that Carter failed to establish he was legally incompetent to stand trial, must be afforded the presumption of correctness.13B.

Given the combined weight of the presumption of correctness and the high burden of proof necessary to justify a nunc pro tunc evidentiary hearing on the question of competency, Carter has failed to demonstrate that the state habeas court erred in denying his allegation of incompetency. Carter relies primarily on the affidavit of Dr. Dorothy Lewis, his board-certified psychiatrist, who concluded that a history of head injuries, mental retardation, and brain damage impaired his ability to make mature judgments, appreciate the consequences of his behavior, and reflect in advance on the appropriateness of his actions. The fact that neither the state habeas court nor the district court discussed this expert opinion does not overcome the presumption of correctness.

First, Lewis did not offer her opinion that Carter was unable to consult with his lawyers with a reasonable degree of rational understanding or was unable to command a rational or factual understanding of the proceedings against him--the minimum standard for a finding that he was incompetent. Therefore, it was not unreasonable for the state habeas court to find this expert testimony unpersuasive.

Furthermore, the state habeas court is entitled to find a defendant competent, despite the introduction of psychiatric testimony diagnosing him as incompetent, without ordering an evidentiary hearing. See, e.g., Maggio, 462 U.S. at 113-18, 103 S.Ct. at 2262-65. Therefore, we previously have found similar expert psychiatric testimony insufficient to satisfy the petitioner's extremely heavy burden of proving a "real, substantial and legitimate doubt" concerning his competency, as required to warrant a nunc pro tunc evidentiary hearing. See, e.g., Williams, 819 F.2d at 607-09. Hence, the Lewis affidavit is not sufficient, without more, to establish the requisite "clear and convincing evidence" necessary to overcome the presumption of correctness, nor does it demonstrate the "real, substantial and legitimate doubt" necessary to warrant a nunc pro tunc evidentiary hearing on the question of competency.

To the contrary, the state habeas court expressly found that Carter's testimony established that he possessed a rational and factual understanding of the proceedings against him. Such a conclusion by a state court, based upon a defendant's testimony, is entitled to a presumption of correctness. See Holmes v. King, 709 F.2d 965, 968 (5th Cir.1983).

Finally, Carter corroborates his claim of incompetency with evidence of physical abuse and neglect and with anecdotal comments made by the prosecutor and defense counsel at trial. Nevertheless, the state habeas court found credible and persuasive the affidavits offered by Carter's court-appointed trial counsel, who stated that they believed he was competent to stand trial and did not think his prior head injuries had impaired his mental competency during the trial. These factual findings are entitled to the presumption of correctness, and the anecdotal evidence is insufficient to overcome this presumption by clear and convincing evidence.

Carter did not contest the voluntariness of his confession, and it thus was admitted into evidence without objection. Nevertheless, he now collaterally attacks the admissibility of the confession on the ground that it was involuntary. His claim is meritless.

A federal court entertaining a collateral challenge to the voluntariness of a confession is obliged to afford a presumption of correctness to state court findings of fact if fairly supported in the record but is authorized to exercise de novo review over the ultimate conclusion of whether, under the totality of the circumstances, the confession was "voluntary."14

Pursuant to Jackson v. Denno, 378 U.S. 368, 84 S. Ct. 1774, 12 L. Ed. 2d 908 (1964), the trial court conducted a hearing on the voluntariness of the confession and entered factual findings, concluding that the confession was freely and voluntarily made. Therefore, we must presume correct the factual determination that the police offered Carter no improper inducements to obtain his confession, nor did they threaten him in order to coerce it. The determination of whether officers engaged in coercive tactics to elicit a confession is a question of fact, and the state court's factual findings are entitled to deference if supported in the record.15

Likewise, the state habeas court entered extensive factual findings concerning the voluntariness of the confession, finding, inter alia, that Carter was timely advised of his Miranda rights; that he understood his rights, yet declined to request the presence of either an attorney or a family member while in custody; that he was offered no inducements to confess and suffered no threats or coercion to extract a confession while in custody; that he was mentally competent and cooperative at the time he made his confession; and that he acknowledged that his statement was made voluntarily. These factual findings are entitled to the presumption of correctness under 28 U.S.C. 2254(d) (1988). To overcome the presumption, Carter must rebut these factual findings by clear and convincing evidence. Id. This he cannot do.

In his federal habeas petition, Carter sought to overcome the factual findings by raising charges of coercion, intimidation, and mental retardation. The district court found, however, that his allegations of coercion and duress were conclusional and unsupported by the evidence adduced at trial or presented by affidavit, and likewise found that the allegation of mental retardation was without merit. This factual determination is adequately supported by the record. Therefore, we must accept as conclusive the state court factual determination that the challenged confession was given voluntarily, not as a product of coercion or intimidation.

Accepting these subsidiary facts as true, we must reach the ultimate question whether Carter's challenged confession was voluntary or constitutionally infirm. The state trial and habeas courts concluded that it was voluntary. Applying pre-AEDPA law, the ultimate question whether a confession is voluntary is a question of law, to be reviewed de novo. See United States v. Scurlock, 52 F.3d 531, 536 (5th Cir.1995).

Coercive police conduct is a necessary prerequisite to the conclusion that a confession was involuntary, and the defendant must establish a causal link between the coercive conduct and the confession. See Colorado v. Connelly, 479 U.S. 157, 163-67, 107 S. Ct. 515, 519-22, 93 L. Ed. 2d 473 (1986). Although mental condition may be a significant factor in the voluntariness calculus, "this fact does not justify a conclusion that a defendant's mental condition, by itself and apart from its relation to official coercion, should ever dispose of the inquiry into constitutional 'voluntariness.' " Id. at 164, 107 S.Ct. at 520.16 Consequently, in the absence of any evidence of official coercion, Carter has failed to establish that his confession was involuntary. See United States v. Raymer, 876 F.2d 383, 386 (5th Cir.1989).

Carter raises a litany of ineffective-assistance-of-counsel claims, urging that his court-appointed trial counsel were constitutionally defective at both the guilt and punishment stages of the trial. Carter is unable, however, to overcome the rigorous burden of proof required to demonstrate ineffective assistance.

A habeas petitioner alleging ineffective assistance must demonstrate both constitutionally deficient performance by counsel and actual prejudice as a result of such ineffective assistance. See Strickland v. Washington, 466 U.S. 668, 687, 104 S. Ct. 2052, 2064, 80 L. Ed. 2d 674 (1984); see also Motley v. Collins, 18 F.3d 1223, 1226 (5th Cir.1994) (summarizing the Washington standard of review). Failure to prove either deficient performance or actual prejudice is fatal to an ineffective assistance claim. Washington, 466 U.S. at 687, 104 S.Ct. at 2064.

To establish deficient performance, the petitioner must prove that the performance of counsel fell below an objective standard of reasonableness. Id. at 688, 104 S.Ct. at 2064-65. Therefore, courts may not fall prey to "the distorting effect of hindsight" but must be "highly deferential" to counsel's performance. Id. at 689-90, 104 S.Ct. at 2065-66. Hence, there is a strong presumption that the performance "falls within the wide range of reasonable professional assistance." Id. at 689, 104 S.Ct. at 2065. Carter has the burden to overcome this presumption.

Moreover, even if counsel's performance was deficient, Carter must affirmatively demonstrate actual prejudice. To do so, he must establish that the attorneys' errors were so deficient as to render the verdict fundamentally unfair or unreliable. See Lockhart v. Fretwell, 506 U.S. 364, 369, 113 S. Ct. 838, 842-43, 122 L. Ed. 2d 180 (1993); Washington, 466 U.S. at 687, 104 S.Ct. at 2064. In evaluating claims of ineffective assistance during the guilt stage of the trial, the petitioner must show a "reasonable probability" that the jury would have otherwise harbored a reasonable doubt concerning guilt. Regarding the sentencing phase, the petitioner must establish a "reasonable probability" that the jury would not have imposed the death sentence in the absence of errors by counsel. Id. at 695, 104 S.Ct. at 2068-69. "A reasonable probability is a probability sufficient to undermine confidence in the outcome." Id. at 694, 104 S.Ct. at 2068.

For purposes of federal habeas review, state court findings of fact made in the course of deciding an ineffectiveness claim are entitled to a presumption of correctness. See 28 U.S.C. § 2254(d) (1988); see also Washington, 466 U.S. at 698, 104 S.Ct. at 2070 (noting that findings of fact are afforded deference); Motley, 18 F.3d at 1226 (same). Unless Carter rebuts them by clear and convincing evidence, therefore, we are required to accept, as conclusive, both the factual findings and the credibility choices of the state courts. See Carter v. Collins, 918 F.2d 1198, 1202 (5th Cir.1990).

The ultimate determination whether counsel was constitutionally ineffective is a mixed question of law and fact that federal habeas courts have traditionally reviewed de novo. See, e.g., Salazar v. Johnson, 96 F.3d 789, 791 (5th Cir.1996); United States v. Faubion, 19 F.3d 226, 228 (5th Cir.1994). Given the holding in Lindh, we must apply this traditional de novo standard to Carter's appeal.

Carter avers that his trial counsel were ineffective because they failed to challenge his competency to stand trial. The state habeas court, however, accorded credibility to counsel's affidavits, averring that they had no reason to believe that Carter was mentally incompetent at the time of trial. Furthermore, the state habeas court found there was insufficient evidence to conclude that Carter was mentally incompetent.

These findings of fact and credibility determinations are entitled to a presumption of correctness, and Carter has not introduced the requisite clear and convincing evidence to prove that they are erroneous. Therefore, because the factual determination that Carter was competent to stand trial is conclusive and binding on us, it necessarily follows that his trial counsel were not constitutionally ineffective in their failure to contest the competency of the defendant to stand trial. "There can be no deficiency in failing to request a competency hearing where there is no evidence of incompetency." McCoy v. Lynaugh, 874 F.2d 954, 964 (5th Cir.1989).

Carter alleges that his counsel might have exposed the alleged "imposter witness" if they had interviewed David Josza prior to trial. Carter did not raise this argument explicitly in the district court, but argues that it is subsumed within his argument that counsel were ineffective in failing to interview government witnesses and adequately to prepare for trial. This vague allegation was not sufficient to place the district court on notice of the claim that Carter now urges, however, and thus the claim is deemed abandoned.17

Furthermore, Carter's argument that his trial counsel "might" have exposed the alleged "imposter witness" is pure speculation, insufficient to overcome the strong presumption of competency and the high burden of actual prejudice required to prove ineffective assistance of counsel. Indeed, given that the contested testimony was merely cumulative and immaterial to the outcome of the trial,18 we cannot conclude that there is a reasonable probability that the jury would have harbored a reasonable doubt about guilt, even if the alleged "imposter witness" had been "exposed" by trial counsel. The voluntary confession precluded any such reasonable doubt, so Carter is entitled to no relief on this claim.

Carter alleges that his trial counsel were ineffective in failing to challenge the admissibility of his confession. But, as we noted previously, the state habeas court accorded credibility to counsel's affidavits, finding that the attorneys were justified in their conclusion that the confession had been given voluntarily and that there were no grounds to object to admissibility. Moreover, both the state trial court and the state habeas court found that the confession was voluntary.

The presumption of correctness attaches to these factual findings and credibility determinations, and Carter cannot overcome it. At a minimum, we cannot conclude that the performance of counsel was "objectively unreasonable." See Washington, 466 U.S. at 688, 104 S. Ct. at 2064-65. Therefore, counsel did not render ineffective assistance of counsel by failing to object, when objection would have been futile.

Carter claims that his trial counsel were defective in their presentation of the "accidental death" defense, whereby they argued that Carter had not actually intended to kill Reyes but had accidentally discharged the weapon during a brief struggle at the cash register. Carter contends that his counsel denigrated the "accidental death" defense during their closing arguments. Furthermore, he argues that his counsel were deficient for failing to propose a jury instruction on the question of accident. These allegations were not adequately presented to the district court, however, and they are deemed waived. See Nichols, 69 F.3d at 1285; Smith, 915 F.2d at 964.

Carter claims that his defense counsel were deficient in failing adequately to investigate the facts of the case and Carter's background; he claims that such an investigation would have produced numerous character witnesses who would have testified during the punishment stage of the trial, as well as expert testimony concerning his mental incapacity. Therefore, Carter contends, the deficient performance of counsel deprived him of mitigating evidence that would have significantly influenced the jury's decision whether to impose the death penalty. The state habeas court found, however, that the testimony of such character witnesses would have been cumulative and would not have been sufficient to change the verdict. We have no reason to question this conclusion.

Given Carter's confession to the crime of murder, we can hardly conclude that the testimony of character witnesses to his reputation as a "good and peaceful person" would have sufficiently impressed the jury to avoid the sentence of death. Consequently, the conclusion of the state habeas court that Carter failed to demonstrate prejudice resulting from the absence of such character witnesses was not error.

As to the allegation that defense counsel were deficient in their failure adequately to investigate mental capacity and to secure expert witnesses who would offer mitigating evidence at the punishment stage, that claim is foreclosed by the factual conclusion that defense counsel were justified in believing that Carter was mentally competent at the time of trial.19 Furthermore, the state habeas court found that there was insufficient evidence to warrant the conclusion that Carter was incompetent in fact at the time of trial, necessarily foreclosing any claim of ineffective assistance predicated on the failure to investigate such alleged incompetency. See McCoy, 874 F.2d at 964.

The duty of trial counsel to investigate is tempered by the information provided to counsel by the defendant. When, as here, the defendant has given counsel reason to believe that certain investigations would be fruitless or harmful, the failure to pursue such investigations may not later be challenged as unreasonable. "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." Washington, 466 U.S. at 691, 104 S.Ct. at 2066. Given that the state courts have concluded that Carter was mentally competent at the time of trial, it necessarily follows that the failure to investigate his mental competency in preparation for trial, or to elicit expert testimony concerning his mental state during the punishment phase of trial, was not ineffective assistance.

Carter argues that his defense counsel were defective in failing to object to the admissibility of his confession to the murder of R.B. Scott, an extraneous offense that was introduced by the prosecution during the punishment stage to justify the imposition of the death penalty. Carter claims there was insufficient evidence to corroborate this confession and insists that it would have been excluded from the jury on a proper objection. Carter concedes, however, that he did not raise this issue in the district court. Therefore, it is deemed waived. See Nichols, 69 F.3d at 1285; Smith, 915 F.2d at 964.20

Carter claims that his trial counsel were deficient in failing to instruct the jury that "deliberate" conduct requires proof of something more than "intentional" conduct under Texas law.21 Carter failed to raise this issue before the district court, however, thereby abandoning it. See Nichols, 69 F.3d at 1285; Smith, 915 F.2d at 964.

Carter charges that defense counsel demonstrated a personal antipathy toward him during their closing arguments in the punishment phase of the trial, thereby prejudicing the jury.22 The state habeas court, however, summarized in great detail counsel's closing arguments, noting that counsel pleaded for mercy and compassion, summarized the arguments against the death penalty, and urged the jury to sentence Carter to life imprisonment rather than death. Therefore, defense counsel did not abdicate their role as advocates, and the state habeas court concluded that their closing arguments did not transgress the "objective standard of reasonableness." Washington, 466 U.S. at 688, 104 S.Ct. at 2064. Having reviewed the record, we agree.

In considering whether counsel's closing argument was ineffective, we consider the closing statements in their entirety. Teague v. Scott, 60 F.3d 1167, 1173 (5th Cir.1995). Furthermore, counsel may make strategic decisions to acknowledge the defendant's culpability and may even concede that the jury would be justified in imposing the death penalty, in order to establish credibility with the jury.23 Although, at the penalty phase, Carter's attorneys acknowledged his culpability and the need for punishment, they also pleaded for mercy and urged the jury to sentence him to life imprisonment rather than death. Consequently, the argument fell within "the wide range of reasonable professional assistance," id. at 689, 104 S. Ct. at 2065, and did not constitute ineffective assistance.

Carter argues that execution of his death sentence, more than fourteen years after his conviction, would violate the Eighth Amendment. We have previously held, however, that such a delay does not offend the Constitution.24 Concluding that the district court correctly refused to issue the writ of habeas corpus, we AFFIRM the judgment and VACATE the stay of execution.