
    Howard MATTHESON, Petitioner-Appellant, v. John T. KING, Secretary of the Department of Corrections, et al., Respondents-Appellees.
    No. 84-3114.
    United States Court of Appeals, Fifth Circuit.
    Jan. 22, 1985.
    
      Matt Greenbaum, New Orleans, La., for petitioner-appellant.
    William R. Campbell, Jr., Susan Scott Hunt, Asst. Dist. Attys., New Orleans, La., for respondents-appellees.
    Before REAVLEY, RANDALL and WILLIAMS, Circuit Judges.
   RANDALL, Circuit Judge:

Howard Mattheson was convicted in a Louisiana court of the first degree murder of Mamie Dupaquier and sentenced to death. After exhausting state remedies, Mattheson filed an amended application for federal habeas relief. On January 16, 1984, the district court denied Mattheson’s amended application and declined to issue a certificate of probable cause to appeal. On April 27, 1984, we granted Mattheson’s motion for a certificate of probable cause to allow him an opportunity to address the merits of his appeal. For the reasons set forth below, we affirm the district court’s denial of the writ of habeas corpus.

I. FACTUAL AND PROCEDURAL HISTORY.

The Louisiana Supreme Court described the details of the crime at length in State v. Mattheson, 407 So.2d 1150, 1155 (La.1981), and we repeat them here only to the extent made necessary by our analysis. On March 9, 1978, Mattheson and his wife, Willene I. Mattheson, entered the Hair Wiz beauty salon in New Orleans. Although the salon was crowded, Mamie Dupaquier, the 75-year-old receptionist, was the sole person in the reception area, located a few feet below the main area. Mattheson, armed with a double-barreled sawed-off shotgun, approached Dupaquier and almost immediately shot her in the head at pointblank range. The blast tore away most of her skull and brain tissue, resulting in her death.

Following the shooting, Mattheson ran up the stairs and ordered the 20-25 people there to lie down on the floor. Mattheson told these people that he had just killed one person and that he would kill again if his orders were not followed. He then directed one of the employees to tape everyone’s hands behind their backs. Mattheson reloaded and, with the help of his wife, began rifling through all of the women’s purses. One woman refused to give up her purse and informed Mattheson that he would have to kill her first. Mattheson responded that he would instead shoot the woman next to her. At that point, Mattheson shot Laura McGoey, who was lying next to the woman refusing to relinquish the purse, in the leg.

Soon thereafter, several more people entered the salon. Mattheson told them that this was not a joke, that one person had already been killed, and that he would not hesitate to kill again. After collecting the money and other valuables, Mattheson and his wife ripped the telephones off the wall and fled. Later that evening, both were apprehended while dining at a nearby restaurant.

At trial, Mattheson’s sole theory of defense was that he lacked the specific intent needed for the commission of first degree murder and that, as a result, the jury should find him guilty of murder in the second degree (felony murder). Under the Louisiana law at that time, a person could be sentenced to death only if he was convicted of first degree murder. In support of his theory, Mattheson testified that on the day of the robbery he had consumed a quart and a half of vodka and was on drugs (LSD). Mattheson though declined to rely on intoxication itself as a reason for his lack of specific intent. Rather, Mattheson, through counsel, argued that the alcohol and drugs had made him clumsy. Mattheson alleged that, when confronted with the gun, Dupaquier had smiled and poked her finger at it, as if she did not believe it was real. She then had pulled the gun toward her, he had pulled back on it, and the gun had accidentally discharged. Mattheson contended that the shooting of McGoey was accidental as well. The jury convicted Mattheson of first degree murder at the guilt phase of the trial and subsequently condemned him to death at the sentencing phase.

The Louisiana Supreme Court on appeal affirmed Mattheson’s conviction and sentence. State v. Mattheson, 407 So.2d 1150 (La.1981). Thereafter, the United States Supreme Court denied Mattheson’s petition for a writ of certiorari. — U.S.-, 103 S.Ct. 3571, 77 L.Ed.2d 1412 (1983). Matthe-son then on August 12, 1983, filed his initial federal habeas action under 28 U.S.C. § 2254, alleging five grounds for relief, only one of which — denial of immunity for Mattheson’s wife to testify — was realleged in the present petition. The District Court for the Eastern District of Louisiana denied the first petition and refused to stay Mattheson’s execution. On appeal we stayed Mattheson’s execution, vacated the district court’s judgment in part, and remanded for further proceedings on Matthe-son’s claim that the state had introduced uncounseled prior convictions at trial, because we could find no basis in the record to determine whether the prior convictions had been uncounseled. Mattheson v. Mag-gio, 714 F.2d 362 (5th Cir.1983). Before the district court could hold an evidentiary hearing on the issue, however, the parties entered into a stipulation to dismiss the action without prejudice pursuant to Federal Rule of Civil Procedure 41(a)(ii).

With the aid of new counsel, Mattheson filed a state habeas action asserting claims identical to those in the present petition. Following an evidentiary hearing on all of Mattheson’s contentions, the state district court denied the petition and set a new execution date. The Louisiana Supreme Court affirmed without opinion. Then, on December 2, 1983, Mattheson filed the instant action, which was summarily denied by the federal district court. Although the state expressly disavowed any reliance on the first federal habeas action as a basis for challenging the present action, the district court, on its own motion and without a hearing, concluded that the petition constituted an abuse of the writ under federal habeas corpus rule 9(b). We again stayed Mattheson’s execution and remanded, this time for a hearing on the issue of abuse of the writ. Mattheson v. King, 721 F.2d 483 (5th Cir.1983).

On remand, the district court consolidated the hearing on abuse of the writ with a hearing on the merits of Mattheson’s ineffective assistance of counsel claim. In a written order following the hearing, the court held first that the petition did not amount to an abuse of the writ and then addressed the merits of the petition. Although recognizing that the findings of the state court on the ineffective assistance of counsel claim carried the presumption of correctness, see 28 U.S.C. § 2254(d), the district court made independent findings of its own and concluded that Mattheson’s counsel was effective. With respect to Mattheson’s other contentions, the district court disposed of them without explanation, stating simply that they were all “without merit.” Mattheson filed a timely notice of appeal, and we granted Mattheson’s motion for leave to appeal in forma pauperis and for a certificate of probable cause.

II. ISSUES ON APPEAL.

Mattheson presents essentially ten issues for appellate review. Mattheson claims his constitutional rights were violated because (1) he was denied the effective assistance of counsel; (2) the trial court’s exclusion of jurors who were unambiguously opposed to imposing the death penalty resulted in a jury that was conviction-prone and unrepresentative of the community; (3) the trial court erroneously refused to grant use immunity to Mattheson’s wife; (4) the state suppressed exculpatory evidence in violation of Brady v. Maryland, 373 U.S. 83, 83 5. Ct. 1194, 10 L.Ed.2d 215 (1963); (5) the firing of the murder weapon in open court rendered the trial fundamentally unfair; (6) the prosecutor in the course of trial made certain remarks and introduced evidence with the sole purpose of inflaming the jury; (7) the method in which the Louisiana Supreme Court reviewed the proportionality of Mattheson’s sentence was inadequate; (8) the death sentence imposed was substantially more severe than the majority of sentences meted out in Louisiana for similar crimes; (9) the imposition of the death sentence would result in Mattheson’s execution while insane; and (10) the death penalty in Louisiana is applied in a racially discriminatory and arbitrary manner.

In his amended petition for habeas relief, Mattheson also asserted that (1) the prosecutor improperly inquired whether Mattheson upon arrest had, indicated to the police that he was intoxicated, and (2) his right of executive review was violated by his death warrant having been signed by a Louisiana district judge rather than by the governor. Mattheson, however, does not press these claims on appeal. We, therefore, deem them abandoned and do not address them. Baker v. Estelle, 711 F.2d 44, 45 (5th Cir.1983), cert. denied, — U.S. -, 104 S.Ct. 724, 79 L.Ed.2d 185 (1984); Davis v. Maggio, 706 F.2d 568, 571 (5th Cir.1983).

We consider each of Mattheson’s contentions asserted on appeal in turn.

III. DISCUSSION.

A. Ineffective Assistance of Counsel.

Mattheson’s principal contention on appeal is that he was denied effective assistance of counsel at both the guilt phase and the penalty phase of the trial. In support of this claim, Mattheson asserts that defense counsel (1) failed to interview the over twenty persons who were at the scene of the crime; (2) failed to conduct any independent pretrial investigation; (3) failed to exercise any peremptory challenges; (4) failed to request any special jury charges; (5) failed to engage in meaningful consultation with Mattheson before trial; (6) failed to investigate Mattheson’s mental state or to seek appointment of a psychiatric, medical, or pharmacological expert; (7) failed to investigate any history of mental instability on Mattheson’s part; (8) referred to Mattheson as a “murderer” during the voir dire and his crime as “gross” and “heinous”; (9) projected an attitude to the jury which disassociated himself from Mattheson; and (10) failed to present any evidence at the sentencing phase, including mitigation witnesses.

1. The Applicable Standards.

The Supreme Court has recently clarified the standard for determining whether counsel’s assistance was so ineffective that the sixth amendment requires the reversal of the defendant’s conviction. In Strickland v. Washington, — U.S. -, 104 S.Ct. 2052, 2064, 80 L.Ed.2d 674 (1984), the Supreme Court held that “[t]he bench mark for judging any claim of ineffectiveness must be whether counsel’s conduct so undermined the proper functioning of the adversarial process that the trial cannot be relied on as having produced a just result.” The Supreme Court established a two-prong test for determining the effectiveness of counsel’s performance:

A convicted defendant’s claim that counsel’s assistance was so defective as to require reversal of a conviction or death sentence 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. 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. Unless a defendant makes both showings, it cannot be said that the conviction or death sentence resulted from a breakdown in the adversarial process that renders the result unreliable.

Id.

In determining the deficiency of counsel’s conduct, the relevant inquiry is whether counsel’s representation fell below an objective standard of reasonableness as informed by prevailing professional standards. Id. at 2065. This assessment of attorney performance requires that conduct be evaluated from counsel’s perspective at the time of occurrence. Because of the difficulties of such an evaluation, the Supreme Court has directed us to “indulge a strong presumption that counsel’s conduct falls within the wide range of reasonable professional assistance; that is, the defendant must overcome the presumption that, under the circumstances, the challenged action ‘might be considered sound trial strategy.’” Id. (citations omitted); see also Knighton v. Maggio, 740 F.2d 1344, 1350 (5th Cir.1984), cert. denied, — U.S. -, 105 S.Ct. 306, 83 L.Ed.2d 241 (1984).

Mere error by counsel, however, even if professionally unreasonable, does not justify setting aside the judgment of a criminal proceeding if the error had no adverse impact on the defense. Thus, the Supreme Court has held that, to assert successfully a claim of ineffectiveness, the defendant must affirmatively prove prejudice. In Strickland, the Court established the requisite amount of prejudice that must be proven in the context of both the guilt phase and the sentencing phase of a death penalty case:

When a defendant challenges a conviction, the question is whether there is a reasonable probability that, absent the errors, the factfinder would have had a reasonable doubt respecting guilt. When a defendant challenges a death sentence such as the one at issue in this case, the question is whether there is a reasonable probability that, absent the errors, the sentencer — including an appellate court, to the extent it independently reweighs the evidence — would have concluded that the balance of aggravating and mitigating circumstances did not warrant death.

Strickland, supra, at 2069. The Court has defined “reasonable probability” as a probability sufficient to undermine confidence in the outcome. Id. at 2068.

As mentioned above, hearings have been held on Mattheson’s ineffective assistance of counsel claim at both federal and state district court levels. Because the deficiency and prejudice prongs of the ineffectiveness inquiry are mixed questions of law and fact, however, we must make an independent determination of whether counsel’s representation passes constitutional muster. Ricalday v. Procunier, 736 F.2d 203, 206 (5th Cir.1984). Of course, to the extent that the state and federal courts made specific predicate factual findings, we must apply the presumption of correctness pursuant to § 2254(d) and the clearly erroneous standard of Federal Rule of Civil Procedure 52(a), respectively. Strickland, supra, at 2070.

2. Analysis.

In Strickland, the Supreme Court stated that, “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. at 2070. With this directive in mind, we turn to Mattheson’s various claims of ineffectiveness.

Although Mattheson has sought at both hearings to show that counsel’s failure to interview witnesses at the scene or to conduct any type of pretrial investigation of the crime fell below reasonable professional standards, Mattheson has not alleged any additional facts pertaining to his case that could have been uncovered by such interviews or additional investigation. At the evidentiary hearing, counsel in fact explained that he had not engaged in pretrial investigation because the essential facts of the crime were widely known and not in dispute; counsel stated that he had felt that conducting an extensive pretrial investigation would not have accomplished anything. Similarly, while Mattheson complains that counsel failed to exercise any peremptory challenges, Mattheson does not identify the juror or jurors that should have been removed by counsel, nor alleges that any were unfavorably disposed to Mattheson. Finally, Mattheson never specifically identifies the inadequacies of the trial court’s instructions or offered the special jury charges that should have been submitted for curative purposes. While several prospective jurors during voir dire admitted to being confused as to the difference between first and second degree murder, there is no allegation that the jury charge as given in any way was deficient in clearly and precisely stating the applicable law. With respect to these allegations, therefore, we conclude that Mattheson has failed to show, not only a reasonable probability of a different outcome, but the slightest adverse impact on the defense or the fairness of the trial. See Larsen v. Maggio, 736 F.2d 215, 217-18 (5th Cir.), cert. denied, — U.S. -, 105 S.Ct. 598, 83 L.Ed.2d 707 (1984); Murray v. Maggio, 736 F.2d 279, 282-83 (5th Cir.1984).

Mattheson also claims that counsel failed to engage in a meaningful consultation with him before trial. At the state court hearing, counsel conceded that he had met with Mattheson briefly only a limited number of times before trial and during pretrial court hearings. We have often held, however, that brevity of consultation time between a defendant and his counsel, without more, cannot support a claim of ineffective assistance of counsel. Murray v. Maggio, supra, at 282. The facts of the instant case were well known to counsel and not complicated. It is moreover undisputed that Mattheson was informed of his counsel’s defense strategy and had agreed to it. Although Mattheson on appeal asserts that counsel during additional meetings could have obtained names of character and mitigation witnesses, counsel at the state hearing stated that as a matter of trial strategy he would not have used such witnesses even if they had been made available to him. Nor does it appear likely that further conversations would have convinced counsel to pursue alternate defenses. At the federal hearing, counsel explained that his meetings with Mattheson left him convinced that Mattheson was both currently sane and in possession of his faculties at the time of the commission of the offense. At the state court hearing, counsel further remarked that he had considered the possibility of an intoxication defense based on Mattheson’s known consumption of alcohol and drugs on the day of the murder, but had rejected it.

Mattheson next asserts that counsel was ineffective in not investigating Mattheson’s past and present mental state and in failing to seek appointment of a psychiatric, medical, or pharmacological expert. According to Mattheson, if counsel had conducted such an investigation, he would have been in a better position to present the mens rea defense of lack of specific intent, a diminished capacity defense, or an insanity plea. Further, the result of a psychiatric examination could have been a significant mitigating factor in the sentencing phase of the trial. Counsel testified, however, that he had investigated Mattheson’s mental background to some extent before trial. He had learned that Mattheson had been previously classified as a dangerous sociopath by the prison psychiatrist in Florida. One psychiatrist, Dr. Kenneth Ridder, told him that, if called to the stand, he would probably have to testify that Mattheson had a sociopathic personality and would probably have little remorse or no remorse for his crime. Although Ridder had not spoken to Mattheson personally, Ridder apparently had consulted with certain colleagues who had. Counsel felt that this psychiatric testimony would be harmful to Mattheson at both the guilt and sentencing phases of the trial and thus decided not to pursue the matter. Moreover, at the evi-dentiary hearings, counsel stated that his own observations of and discussions with Mattheson, as well as the details of the crime, convinced him not to pursue an investigation into Mattheson’s mental state. Counsel stated that Mattheson appeared completely sane and aware at their pretrial conferences. With respect to the commission of the crime, counsel knew that Mattheson had consumed some alcohol and LSD but believed based on discussions with Mattheson that his intoxication was not great enough to eviscerate intent. Indeed, at the state court hearing, Mattheson himself admitted that he had told counsel only that the shooting was the result of an accident; Mattheson does not allege that he suggested to counsel that his intoxication prevented him from forming the requisite specific intent.

We believe that counsel’s decision not to investigate further either Mattheson’s mental history or his mental state at the time of the offense or the trial falls within the realm of sound trial strategy. Counsel could have reasonably believed that expert testimony describing Mattheson as a violent sociopath would not have been regarded as a mitigating factor by the jury at the sentencing hearing. Mattheson himself gave counsel no direct indication that he was presently insane or that he was so intoxicated at the time of the offense that he was incapable of forming the specific intent needed to commit first degree murder. Indeed, the specifics of Mattheson’s activity at the Hair Wiz salon belie such a notion. The evidence adduced at trial reveals that Mattheson brought tape with him to tie up the customers, reloaded his gun after discharge, methodically robbed the persons at the salon, and ripped the telephone from the wall to prevent anyone from calling for help. Once home, Mattheson changed clothes, hid his weapon under the mattress, and went out again to a restaurant. Given these facts, counsel could have reasonably concluded that the best defense available was that the alcohol and drugs merely contributed to the accident by impairing Mattheson’s judgment. See Martin v. Maggio, 739 F.2d 184, 187 (5th Cir.1984) (details of the crime made it unlikely that juror would have acquitted defendant on thesis of lack of criminal intent). In Strickland, the Supreme Court stated: “[W]hen a defendant has given counsel a reason to believe that pursuing certain investigations would be fruitless or even harmful, counsel’s failure to pursue those investigations may not later be challenged as unreasonable.” 104 S.Ct. at 2066. In light of the fact that counsel here was given reason to believe that the results of an investigation into Mattheson’s mental health would have been detrimental to his defense, we hold that Mattheson has failed to rebut the presumption that counsel’s actions were reasonable under the circumstances.

Mattheson next contends that certain remarks made by counsel at voir dire without Mattheson’s consent prejudiced the jury against him and had the effect of disassociating him from his counsel. Specifically, Mattheson complains that counsel (1) told the jury that he was appointed by the court, (2) referred to Mattheson as a “murderer” and (3) described the crime as “gross” and “heinous.” While, at first glance, these comments, taken together, seem patently unreasonable, we think that under the circumstances of this particular case they did not fall below prevailing professional norms. At the federal district court hearing, counsel explained that he often told the jury that he was appointed in order to account for the absence of certain kinds of evidence, the cost of which precluded presentation. Counsel further stated that, because of the overwhelming evidence of Mattheson’s guilt, he had decided to be as candid as possible with the jury, presumably to build up his credibility and that of his theory of the case. Thus, to this end, counsel admitted that Mattheson was a murderer and that the act was in fact heinous and gross, but argued that, at the moment of the weapon’s discharge, Mattheson lacked the specific intent needed for a conviction of first degree murder and thus should only be convicted of murder in the second degree. Applying the presumption that the challenged action was taken as a matter of sound trial strategy, we cannot say that counsel’s remarks viewed in this context were outside the wide range of professionally competent assistance.

Mattheson’s finally argues that counsel, in deciding not to present any evidence at the penalty phase of the trial, provided ineffective assistance of counsel. We have recently held in similar cases that such a determination, if based on an informed and reasoned practical judgment, is well within the range of practical choices not to be second-guessed. Milton v. Procunier, 744 F.2d 1091, 1099 (5th Cir.1984); Knighton v. Maggio, supra, at 1350. In this case, however, it is not clear to what extent counsel investigated the possibility of mitigating evidence or even whether he discussed the subject with Mattheson before trial. Nonetheless, even assuming that counsel’s performance was deficient in this respect, we find Mattheson’s claim to be without merit because we do not think there is a reasonable probability that, but for counsel’s alleged unprofessional errors, the result of the trial would have been different. Mattheson has failed at both the state post-conviction evidentiary hearing and at the federal habeas evidentiary hearing to present or describe the testimony of any witness that would show that counsel’s performance precluded the introduction of mitigating evidence that would have had a significant impact on the jury. Instead, even at this late date, Mattheson merely makes essentially conclusory allegations that, if given a chance, several witnesses— his landlord, two doctors and one nurse he knew in prison, a prison minister, and a sister-in-law — would have supplied some mitigating, although unspecified, testimony. Such allegations, standing alone, especially in light of the striking aggravating circumstances of the case, do not satisfy the prejudice component of the Strickland test. In Larsen v. Maggio, we stated: “The hypothetical or theoretical ‘might have beens’ at a trial do not justify the issuance of a Writ. Rather, the petitioner must demonstrate that the ‘might have beens’ would have been important enough to affect the proceedings’ reliability.” 736 F.2d at 218. Here, Mattheson has simply failed to offer any evidence that would indicate a reasonable probability exists that, absent the errors, the jury would have concluded that the balance of aggravating and mitigating circumstances did not warrant death.

In sum, Mattheson has failed to show that any of counsel’s asserted errors were both deficient and prejudicial. We therefore conclude that Mattheson is not entitled to habeas relief on the ground of ineffective assistance of counsel.

B. The Death-Qualified Jury.

Mattheson next contends that the process of excluding from the guilt phase of the trial prospective jurors who are unwilling to consider imposing capital punishment resulted in a jury that was impermissibly guilt-prone and unrepresentative of the community. We have recently considered and rejected this exact claim. Knighton v. Maggio, supra, at 1351; Moore v. Maggio, 740 F.2d 308, 321 (5th Cir.1984); Willie v. Maggio, supra, at 1384-85; Sonnier v. Maggio, 720 F.2d 401, 407-08 (5th Cir.1983), cert. denied, — U.S. -, 104 S.Ct. 1331, 79 L.Ed.2d 726 (1984); Smith v. Balkcom, 660 F.2d 573, 575-84 (5th Cir.1981), modified on other grounds, 671 F.2d 858 (5th Cir.), cert. denied, 459 U.S. 882, 103 S.Ct. 181, 74 L.Ed.2d 148 (1982); Spinkellink v. Wainwright, 578 F.2d 582, 583-96 (5th Cir.1978), cert. denied, 440 U.S. 976, 99 S.Ct. 1548, 59 L.Ed.2d 796 (1979).

Mattheson, however, attempts to distinguish these cases on two grounds. First, Mattheson argues that more recent studies provide stronger empirical evidence that death-qualified jurors are biased in favor of conviction and tend to belong to certain discrete groups. Second, Mattheson argues that he, unlike the petitioner in Smith, is not arguing that only those unequivocally committed to imposing the death penalty should be excluded for cause from the guilt phase of the trial, but that no juror who states under oath that he can apply the law fairly and impartially despite his feelings should be so excluded. We find these grounds insufficient to avoid the application of our precedent. Our rulings in the cases cited above were in no way dependent on the quantum of proof presented or on the fact that the petitioner happened to assert the additional argument that prospective jurors strongly in favor of the death penalty should be excluded for cause at the guilt phase. Rather, in those cases we held that “a ‘death-qualified’ jury does not deprive a defendant of a fair and impartial jury even assuming that defendant showed that such a jury, on the average, would be more likely to favor the prosecution.” Sonnier, supra, at 407. We also held as a matter of law that “unalterable opposition to the death penalty is a legitimate disqualification and that the exclusion of such disqualified jurors does not violate the fair cross-section principle of the sixth amendment.” Smith, supra, at 583. Mattheson’s attack on the composition of his jury is thus without merit.

C. Use Immunity.

Mattheson next contends that his constitutional rights of compulsory process and due process were violated by the trial court’s refusal to grant his wife, Willene I. Mattheson, use immunity. As mentioned above, Mattheson’s defense at trial was that his gun accidentally discharged when Dupaquier grabbed the weapon and pulled it toward her. Because the reception area was several feet below the main area, however, the only persons in the salon who saw the shooting, and thus who could corroborate Mattheson’s story, were a 13-year-old girl and Willene Mattheson. At trial, the 13-year-old girl testified that she had not seen Dupaquier grab for the gun, although she conceded at cross-examination that her attention had been focused primarily on Mattheson and not on the receptionist. Willene Mattheson, the only defense witness other than Mattheson called to the stand, refused to testify, asserting instead her fifth amendment right to refuse to answer any questions concerning the homicide. After the trial court denied counsel’s request for use immunity, Willene’s attorney testified outside the presence of the jury that, in his opinion, her testimony would have been exculpatory and critical.

In support of his argument that the exculpatory and the essential nature of the testimony required the granting of use immunity, Mattheson cites Government of Virgin Islands v. Smith, 615 F.2d 964 (3d Cir.1980), in which the Third Circuit held that, when a defense witness has essential exculpatory evidence, the defendant is entitled to the immunized testimony unless the grant of immunity is outweighed by a strong government interest. We, however, have already rejected this argument and declined to follow the Third Circuit case. Autry v. Estelle, 706 F.2d 1394, 1401 (5th Cir.1983); United States v. Chagra, 669 F.2d 241, 258-59 (5th Cir.), cert. denied, 459 U.S. 846, 103 S.Ct. 102, 74 L.Ed.2d 92 (1982); United States v. Thevis, 665 F.2d 616, 639-41 (5th Cir.), cert. denied, 459 U.S. 825, 103 S.Ct. 57, 74 L.Ed.2d 61 (1982); see also United States v. Turkish, 623 F.2d 769, 778 (2d Cir.1980), cert. denied, 449 U.S. 1077, 101 S.Ct. 856, 66 L.Ed.2d 800 (1981). In Thevis, we held that, absent prosecutorial misconduct, separation of power concerns and the possibility of abuse preclude federal district courts from granting immunity to a defense witness merely because that witness has essential exculpatory information unavailable from other sources. We stated:

[T]he immunity decision requires a balancing of public interests which should be left to the executive branch. While a grant of use immunity theoretically does not improve the legal position of the person immunized, in that he still can be prosecuted for his crime, in practice the burden placed on the government to prove that any evidence obtained against the immunized suspect is not tainted by the suspect’s statement can significantly impair future prosecutions____ An immunity decision, moreover, would require a trial judge, in order to properly assess the possible harm to public interests of an immunity grant, to examine pre-trial all the facts and circumstances surrounding the government’s investigation of the case. Such collateral inquiries would necessitate a significant expenditure of judicial energy, possibly to the detriment of the judicial process overall, and would risk jeopardizing the impartiality and objectivity of the judge at trial.

665 F.2d at 639-40. This holding was applied to the § 2254 habeas context in Au-try, supra, where we held that principles of federalism required giving the state prosecutor no less discretion in determining whether to immunize a witness than that enjoyed by federal prosecutors under article II of the Constitution. 706 F.2d at 1402. Although in Autry we indicated that a constitutional right to immunized testimony might exist to remedy prosecutorial abuse, Mattheson himself explicitly disavows that any prosecutorial misconduct existed here to warrant the granting of immunity. We therefore hold that the trial court’s refusal to grant use immunity was not constitutional error.

D. The Brady Claim.

Mattheson next contends that his constitutional rights under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), were violated by the state's failure to disclose the existence of several vodka bottles seized by state officials in a search of his apartment. Mattheson testified at trial that on the day of the shooting he drank a quart and a half of vodka and that previously he had been drinking a quart a day. This drinking, according to Mattheson, impaired his judgment and was a significant factor in the accidental firing of his weapon. Mattheson on appeal alleges further that his drinking problem was a mitigating circumstance, any evidence of which should have been presented to the jury in the sentencing phase of the trial. That the empty bottles were found in his apartment is alleged to constitute exculpatory corroborating evidence of both Mattheson’s mental impairment and drinking habits.

In Brady, the Supreme Court held that suppression by the prosecutor of evidence favorable to an accused violates due process when the evidence is material either to guilt or to punishment, irrespective of the good or bad faith of the prosecutor. Id. at 87, 83 S.Ct. at 1196. The prosecutor, however, has no duty to make a complete and detailed accounting of all investigatory work on a case to defense counsel. United States v. Agurs, 427 U.S. 97, 109, 96 S.Ct. 2392, 2400, 49 L.Ed.2d 342 (1976). For example, when the information is fully available to the defendant and his reason for not obtaining and presenting the information is his lack of reasonable diligence, the defendant has no claim under Brady. United States v. Dean, 722 F.2d 92, 95 (5th Cir.1983); United States v. Jones, 712 F.2d 115, 122 (5th Cir.1983). In the instant case, Mattheson concedes that he knew of the bottles. Moreover, he stated at the state post-conviction evidentiary hearing that he informed counsel of their existence. Although counsel stated later at that same hearing that he did not remember being so informed, he did testify that he had been told of Mattheson’s drinking on the day of the murder. Finally, a photograph of Mattheson’s apartment was entered into evidence which prominently displayed an empty vodka bottle. Pretermitting other problems with Mattheson’s claim, we find based on these facts that Mattheson’s failure to present evidence of the existence of the vodka bottles was due to his own lack of diligence and that of his counsel, and not the state’s violation of due process.

E. Evidentiary Matters.

Mattheson further complains that he was denied his constitutional rights by the admission, over his counsel’s objections, of highly prejudicial evidence designed solely to inflame the jury. Specifically, Mattheson alleges that the state court erred in (1) permitting the state to fire the murder weapon in open court, (2) admitting testimony graphically describing the injury to the victim, and (3) admitting evidence pertaining to the second shooting by Mattheson.

In reviewing state evidentiary rulings, our role is limited to determining whether a trial judge’s error is so extreme that it constituted denial of fundamental fairness. Bailey v. Procunier, 744 F.2d 1166, 1168 (5th Cir.1984). Thus, “[w]e do not sit as a super state supreme court to review error under state law.” Skillern v. Estelle, 720 F.2d 839, 852 (5th Cir.1983), cert. denied, — U.S.-, 105 S.Ct. 224, 83 L.Ed.2d 153 (1984). We have held that “the erroneous admission of prejudicial testimony justifies habeas corpus relief only when it is ‘material in the sense of crucial, critical, highly significant factor.’ ” Bailey, supra, at 1168-69 (quoting Skillern, supra, at 852).

Applying this standard, we think it is clear that none of the alleged evidentiary errors asserted by Mattheson was sufficiently egregious to render his trial fundamentally unfair. Given the immense quantity of incriminating evidence presented at trial, the discharge of the firearm in open court can hardly be considered a “crucial, critical, highly significant factor” in Mattheson’s ultimate conviction and sentence. Similarly, even if we were to assume that the district court erred in permitting testimony to the effect that Dupaquier’s scalp was “blown off” by the blast, we could not say that any resulting prejudice was of constitutional magnitude requiring the reversal of Mattheson’s conviction. Finally, we agree with the Louisiana Supreme Court that the fact of and the circumstances surrounding the second shooting were highly probative of Mattheson’s specific intent to kill and his state of intoxication. Such evidence, therefore, was properly admitted and did not result in unfair prejudice.

F. Prosecutorial Misconduct.

Mattheson next contends that he is entitled to habeas relief because of certain inflammatory and prejudicial remarks made in the course of the prosecutor’s closing argument. During his closing argument, the prosecutor told the jury that Dupaquier had had her head blown off and that “Dupaquier head’s in the ceiling.” The prosecutor also commented that, if the jury believed Mattheson to be guilty of second degree murder, he “can continue to do what Dupaquier cannot continue to do: wake up each morning and draw a breath.”

In reviewing the propriety of a prosecutor’s comments made during a state trial, we apply the same basic standard used in reviewing a state court’s evidentia-ry rulings. We may overturn a state court conviction or sentence only if the alleged error made the trial fundamentally unfair. Donnelly v. DeChristoforo, 416 U.S. 637, 642, 94 S.Ct. 1868, 1871, 40 L.Ed.2d 431 (1974); Willie v. Maggio, supra, at 1390; O’Bryan v. Estelle, 714 F.2d 365, 387 (5th Cir.1983), cert. denied, — U.S.-, 104 S.Ct. 1015, 79 L.Ed.2d 245 (1984). Here, in light of the arguments presented and all the evidence adduced at trial, we do not think that the prosecutor’s reference to Dupaquier’s head as having been blown off and in the ceiling rendered the trial unfair. The remarks, although unnecessarily graphic, were an accurate account of what happened. See Cronnon v. State of Alabama, 587 F.2d 246, 251 (5th Cir.) (“It would be an insult to all known physical facts to suggest that the blood did not ‘squish.’ ”), cert. denied, 440 U.S. 974, 99 S.Ct. 1542, 59 L.Ed.2d 792 (1979). With respect to the prosecutor’s other remark quoted above, we think that the prosecutor acted improperly in suggesting to the jury that it should find Mattheson guilty of first degree murder so that the death penalty may be imposed. We do not believe, however, that any prejudice that resulted, viewed in the context of the entire trial, was so egregious as to violate the Constitution. The suggestion made by the prosecutor was an isolated occurrence that did not render the trial fundamentally unfair.

G. Proportionality.

Mattheson attacks his sentence on the ground that the Louisiana Supreme Court unconstitutionally limited its proportionality review to a parish-wide, rather than a state-wide, analysis. This claim is meritless. The Supreme Court has recently held that a defendant does not have a constitutional right to any type of proportionality review, at least as long as the state’s capital sentencing scheme sufficiently minimizes arbitrary and capricious sentencing. Pulley v. Harris, — U.S. -, 104 S.Ct. 871, 79 L.Ed.2d 29 (1984). We have held previously that the Louisiana system of review satisfies constitutional requirements. Martin v. Maggio, 711 F.2d 1273, 1284, 1286 (5th Cir.1983); Williams v. Maggio, 679 F.2d 381 (5th Cir.1982) (en banc), cert. denied, — U.S.-, 103 S.Ct. 3553, 77 L.Ed.2d 1399 (1983).

Mattheson also alleges that his sentence is disproportionate in fact to other sentences meted out across the state for like offenses. We once again find the Supreme Court case of Pulley v. Harris dispositive of Mattheson’s claim. In Pulley, the Supreme Court distinguished between traditional proportionality analysis that abstractly evaluated the appropriateness of a sentence for a particular crime and the comparative type of proportionality analysis that examines whether the penalty is unacceptable in a particular case because it is disproportionate to the punishment imposed on others convicted of the same crime. With respect to this latter inquiry, which is the basis of Mattheson’s claim here, the Court held that the Constitution did not require that each death sentence be strictly proportionate to other sentences imposed across the state as long as sufficient checks were in place to rationalize the sentence by minimizing the risk of arbitrary or capricious action. 104 S.Ct. at 880-81. As noted above, we have already determined that the Louisiana sentencing system, including the parish-wide proportionality review systematically conducted by the Louisiana Supreme Court in all death penalty cases, passes constitutional muster. Williams, supra, at 395.

H. Insanity.

Mattheson next asserts that his execution should be stayed because of his present insanity. In connection with this claim, he seeks an evidentiary hearing to present evidence sufficient to raise a reasonable doubt as to his capacity to proceed. Mattheson, however, has already received and through counsel participated in an evidentiary hearing in state court regarding his sanity. At this hearing, the only evidence introduced by Mattheson to show his present mental state was five letters he had written to his counsel from prison. Although these letters are not in the record, the state court noted that they cite cases, make cogent legal arguments, and, in the state court’s opinion, generally demonstrate that Mattheson was thinking clearly. The sole expert to testify at the hearing was state witness Dr. Aris Cox, a physician specializing in forensic psychiatry. Based on his examination of Mattheson, Dr. Cox concluded that, while Mattheson was depressed and had some sort of mental disturbance, he was in contact with his environment and was aware of his situation, the purpose of the hearing, and the consequences facing him if he was unsuccessful. The state court made the following findings and conclusions:

Based on the records submitted to this Court, ... the letters of Mr. Mattheson as I previously stated and again by Dr. Cox’s testimony I don’t feel that Mr. Mattheson is in such a mental state as to appoint a lunacy commission, [not] at all do I feel Mr. Mattheson is in such a mental state that he does not know his surroundings, that he does not know who you are, that he cannot assist in his petition. I feel that Mr. Mattheson at the present time is sane.

Based on the evidence admitted at the hearing, we find the district court’s findings to be supported by the record and apply a presumption of correctness to those findings. 28 U.S.C. § 2254(d); Maggio v. Fulford, 462 U.S. 111, 103 S.Ct. 2261, 76 L.Ed.2d 794 (1983). In so doing, we of course realize that the state court only found that Mattheson had the indicia of sanity at the time of the hearing. Nevertheless, because Mattheson has not alleged any change of condition or circumstance that would lead us to believe that he is any less competent today than he was at the time of the hearing, we are compelled to accept the state court’s evaluations of competency as currently applicable. See Holmes v. King, 709 F.2d 965, 968 (5th Cir.), cert. denied, — U.S.-, 104 S.Ct. 428, 78 L.Ed.2d 362 (1983). We thus defer to the state court’s conclusion and reject Mattheson’s claim.

I. Discriminatory Application of the Death Penalty.

Finally, Mattheson contends that his death sentence is violative of the eighth and fourteenth amendments because it is being administered in a racially discriminatory fashion, based solely on the race of the victim. Mattheson, however, did not adduce any evidence to support this allegation at the state post-conviction evidentiary hearing and suggested no evidence to the federal district court that would take into account nonracial variables in the sentencing decision. Without a more complete statistical proffer, Mattheson is not entitled to relief or an evidentiary hearing. Moore v. Maggio, supra, at 323; Smith v. Balkcom, 671 F.2d 858, 859-60 (5th Cir.1982); see also Spinkellink v. Wainwright, supra, at 614.

IV. CONCLUSION.

We have examined each of Mattheson’s claims a,nd conclude that he is not entitled to habeas relief. Accordingly, the judgment of the district court is AFFIRMED and the stay of execution is VACATED. 
      
      . Mattheson’s case was severed from his wife’s case.
     
      
      . At the time Mattheson committed the crime, the relevant statutes read as follows:
      La.R.S. 14:30. First Degree Murder
      First degree murder is the killing of a human being when the offender has a specific intent to kill or to inflict great bodily harm.
      Whoever commits the crime of first degree murder shall be punished by death or life imprisonment at hard labor without benefit of parole, probation, or suspension of sentence in accordance with the recommendation of the jury.
      La.R.S. 14:30.1. Second Degree Murder
      Second degree murder is:
      A. The killing of a human being when the offender is engaged in the perpetration or attempted perpetration of aggravated rape, aggravated arson, aggravated burglary, aggravated kidnapping, aggravated escape, armed robbery, or simple robbery, even though he has no intent to kill____
     
      
      . Although the trial judge gave the jury an intoxication instruction, Mattheson's counsel several times made it clear to the jury that Mattheson was not asserting that his intoxication alone was the reason that he lacked the specific intent necessary for the commission of first degree murder. Indeed, at one point during closing arguments, Mattheson’s counsel stated that such a defense "would be incredible.” Trial Tr., Vol. II, at 481.
     
      
      . We stated:
      The district court’s dismissal of appellant’s petition for a writ of habeas corpus under Rule 9(b) without a hearing and on the basis of what is, in effect, a one sentence order is reversed. The case is remanded to the district court with instructions to hold a hearing on the issue of abuse of the writ. Without intending to foreclose an independent and careful consideration by the district court on that issue, this court notes that it has serious misgivings about whether an order holding that appellant had abused the writ would be sustainable if appellant is able to establish at that hearing the facts suggested in his motions to this court.
      721 F.2d at 483.
     
      
      . We have often noted, and repeat again here, that in a capital case it is essential that a district court set forth those specific findings of fact and conclusions of law that underlie its ultimate disposition of the case. While to do so may result in some delay, the findings and conclusions serve the interest of both the state and the defendant by facilitating prompt and effective appellate review. See Willie v. Maggio, 737 F.2d 1372, 1377 (5th Cir.1984).
     
      
      . The district court denied in forma pauperis status and a probable cause certificate "for reasons implicit in [the] ruling in this matter." Record Doc. 15.
     
      
      . Mattheson’s amended petition alleges:
      Petitioner’s Fifth, Eighth, and Fourteenth Amendment rights were violated by the prosecution’s question to the petitioner on cross-examination which sought to imply that Mr. Mattheson was guilty because he did not raise the defense of intoxication at the time of his arrest. Although the prosecutor withdrew the question after the Court had overruled an objection to it, the inference left for the jury was clear.
     
      
      . Mattheson’s amended petition alleges:
      Petitioner’s right to executive review prior to the signing of any death warrant, which right is preserved by Article I, Section 24 of the Louisiana Constitution of 1974, was violated when the death warrant in this case was signed by the district judge, rather than the Governor of the State of Louisiana. (To be established at the hearing on this Application).
     
      
      . Mattheson’s amended petition alleges:
      Petitioner’s Sixth, Eighth, and Fourteenth Amendment rights were violated, because the legal assistance rendered to him by counsel at both the guilt and sentencing stages of his capital trial was completely ineffective. The legal assistance rendered to petitioner by trial counsel fell below reasonable standards, and prejudiced petitioner by depriving him of meritorious defenses at both stages of trial.
     
      
      . Mattheson also makes three other claims: (1) counsel failed to seek a new trial on the basis that the prosecution improperly suppressed exculpatory evidence; (2) counsel failed to seek suppression of evidence seized during the search incident to arrest or the subsequent warranted search of Mattheson’s apartment; and (3) counsel failed to move for a change of venue. The first two of these claims, however, were not asserted on appeal and thus are abandoned. See Baker, supra; Davis, supra. The latter claim was not presented to the district court and therefore will not be considered on appeal. See Willie, supra, at 1387-88 n. 20; Bufalino v. Reno, 613 F.2d 568, 569 n. 1 (5th Cir.1980).
     
      
      . For example, Mattheson alleges that counsel failed to interview the arresting police officers, to examine the scene of the crime, or to consult with ballistics or forensic experts. Counsel’s alleged failure to investigate Mattheson’s mental state or any mitigating circumstances surrounding the crime or Mattheson’s life in general is independently discussed infra.
      
     
      
      . Mattheson also alleges that counsel failed to prepare adequately for trial. Counsel testified at the state post-conviction evidentiary hearing that he had only spent twenty hours in preparation for Mattheson’s trial. This claim, however, seems to overlap with Mattheson’s more specific claims of counsel’s ineffectiveness. To the ex-, tent the claim asserts a discrete error by counsel, it must fail since Mattheson does not allege how counsel’s failure to prepare adequately resulted in sufficient prejudice to undermine confidence in the result of the trial.
     
      
      . In his brief, Mattheson notes that the district court found that counsel was not deficient and thus never reached the issue of prejudice. Mattheson asked us to remand the case back to the district court for an evidentiary hearing on the prejudice issue. We deny this request. Any determination of prejudice by the district court would be subject to our independent review. Moreover, at the time of the hearing in district court, although the Supreme Court decision in Strickland had yet to be announced, it was the firm law in this Circuit that the habeas petitioner claiming ineffectiveness had the burden of demonstrating some actual adverse impact in addition to some error of counsel. See United States v. Cockrell, 720 F.2d 1423, 1426 (5th Cir. 1983), cert. denied, — U.S.-, 104 S.Ct. 3534, 82 L.Ed.2d 839 (1984); Boyd v. Estelle, 661 F.2d 388, 389-90 (5th Cir.1981). Thus, Mattheson, in presenting his evidence to the trial court, had both ample notice of the need and the opportunity to show prejudice. See Ricalday, supra, at 206 n. 1 ("the fact that the district court decided Ricalday’s habeas claim under slightly different standards does not require a redetermination by that court of the petitioner's claim”).
     
      
      . In his brief, Mattheson intimates that a psychiatric examination could have turned up additional information that could have been used in his defense or as a mitigating circumstance at trial. In neither of the evidentiary hearings that have been held on the ineffective assistance of counsel claim, however, has Mattheson presented any specific evidence that would have made an impact if admitted at trial. Mere conclusory allegations by counsel that Mattheson would have been judged incompetent or mentally impaired is not sufficient to meet the Strickland requirement that the defendant affirmatively prove prejudice. See Willie, supra, at 1394.
     
      
      . In holding that counsel’s conduct was not deficient under Strickland, either in regard to his failure to investigate Mattheson's mental state or in his remarks made at voir dire, we have also considered the testimony of four of counsel’s peers introduced at the federal habeas evidentiary hearing. We do not find their testimony persuasive evidence that counsel’s performance was unreasonable for several reasons. First, we note that the witnesses had not read the trial transcript but testified for the most part only in response to hypothetical questions. Second, the witnesses were often equivocal in their answers, not distinguishing clearly between professionally unreasonable conduct and unsuccessful or poor strategy. Finally, any evaluation of the testimony must be informed by the district court’s finding that "[the witnesses'] after-the-fact appraisals are less credible ... than the straight forward description of the way in which [counsel] went about discharging his responsibilities.” In light of all the circumstances, we do not feel that the testimony of these witnesses was sufficient to rebut the strong presumption of professionally reasonable conduct.
     
      
      . We, however, point out that it is by no means clear that counsel’s conduct was deficient. At the evidentiary hearing, counsel remarked that at the time of the trial he had thought that there was little mitigating evidence available. He also testified that, in any event, he did not investigate the possibility of introducing such evidence since to do so would have opened the door to repeated damaging cross-examinations on Mattheson’s criminal record and general character.
     
      
      . Mattheson apparently asserts this argument twice in his amended habeas petition. Claim II of the petition alleges:
      Petitioner’s Sixth, Eighth and Fourteenth Amendment rights were violated when the Court submitted the general'venire to a process of "death-qualification” over the objection of trial counsel. The resulting exclusion for cause of prospective jurors rendered the ultimate jury which convicted and sentenced him: non-neutral; partial on the issue of guilt; unconstitutionally prone to convict him and sentence him to death; and unrepresentative of the' community.
      Claim III alleges:
      Petitioner's Eighth and Fourteenth Amendment rights were violated by the exclusion for cause at his trial of three jurors who did not make it unequivocally clear that they could impose death as a punishment. See, Taylor v. Louisiana, 419 U.S. 522, 95 S.Ct. 692, 42 L.Ed.2d 690 (1975).
      In his brief, Mattheson states explicitly that ”[i]t is not the petitioner’s position that the excluded jurors should not have been excused for cause as to the sentencing phase.” Appellant’s Brief, at 30. Mattheson thus does not argue, at least on appeal, that the excluded jurors were not sufficiently unequivocal in their opposition to capital punishment to warrant exclusion under the Supreme Court's holding in Witherspoon v. Illinois, 391 U.S. 510, 88 S.Ct. 1770, 20 L.Ed.2d 776 (1968).
     
      
      . In support of this contention, Mattheson cites Grigsby v. Mabry, 569 F.Supp. 1273 (E.D.Ark. 1983), incorporates by reference the scientific studies discussed therein, and refers to additional studies that have become available since the Grigsby decision.
     
      
      . Mattheson's amended petition alleges:
      Petitioner’s Eighth and Fourteenth Amendment rights have been violated by the trial court’s refusal to grant petitioner’s wife immunity from prosecution for testimony given at either the guilt or sentencing phase of the trial, even though evidence was adduced on the record to the effect that Mrs. Mattheson was in possession of exculpatory facts which could have had a bearing on the verdict or on the punishment arrived at thereafter.
     
      
      . Máttheson’s amended petition alleges:
      Petitioner’s Sixth, Eighth and Fourteenth Amendment rights were violated by the State’s failure to disclose exculpatory evidence (i.e. numerous vodka bottles discovered in petitioner’s apartment) which would have verified petitioner’s otherwise uncorroborated intoxication defense which was utilized in both phases of his trial. (To be established at the hearing on this Application).
     
      
      . The Louisiana Supreme Court, in considering this claim, held that the evidence was not so material that it would have produced a different result. The court noted that the photograph admitted into evidence and the vodka bottle pictured therein corroborated Mattheson’s testimony concerning his intoxication. Information of the liquor bottles, therefore, while corroborative, was held not to be sufficiently material to require disclosure under Brady. 407 So.2d at 1167.
     
      
      . Mattheson’s amended petition alleges:
      Petitioner's Eighth and Fourteenth Amendment rights were violated when the state was permitted to fire in open court the gun which had caused the homicide, even though there was no question as to its identity or its ability to operate properly.
     
      
      . Mattheson's amended petition alleges:
      Petitioner’s Eighth and Fourteenth Amendment rights were violated by the introduction of highly prejudicial evidence at the guilt phase of his trial, including testimony regarding the post-homicide wounding of Ms. McGoey, in that said evidence was aimed solely at establishing proof that the crime was committed in an "especially heinous, atrocious or cruel manner" — and, accordingly, the introduction of such evidence should have awaited the sentencing phase of the trial.
     
      
      . We note in passing that the record reveals that defense counsel refused to stipulate that the weapon was operational and sought instead to require the state to prove the fact through live testimony.
     
      
      . Mattheson's amended petition alleges:
      Petitioner’s Eighth and Fourteenth Amendment rights were violated when the State introduced and constantly harped upon evidence which had as its sole purpose the inflaming of the petit jury. Said evidence included the numerous references to the "blowing-off” of the victims scalp; constant references to a shooting which occurred after the homicide in question; and the prosecutor’s closing remarks to the jury to the effect that if they subscribed to petitioner’s theory that he was only guilty of second-degree murder, the defendant "can continue to do what [the victim] cannot continue to do: wake up each morning and draw a breath.”
     
      
      . Mattheson also complains that the prosecutor made repeated references to the second shooting. We have already held, however, that the second shooting was highly probative of the central issue in the case: the existence of the specific intent to kill.
     
      
      . Mattheson’s amended petition alleges:
      Petitioner’s Eighth and Fourteenth Amendment rights were violated because the method of reviewing his sentence of death for proportionality utilized by the Louisiana Supreme Court was unconstitutionally limited to a parish-only, rather than statewide comparison, and was insufficient to assure that petitioner's death sentence is consistent with other sentences meted out across the state for similar offenses. See, Harris v. Pulley, 692 F.2d 1189, 1196-97 (9th Cir.1982), cert. granted, 460 U.S. 1036, 103 S.Ct. 1425, 75 L.Ed.2d 787 (1983).
     
      
       Mattheson’s amended petition alleges:
      Petitioner’s Eighth and Fourteenth Amendment rights were violated because his sentence of death is inconsistent with and substantially more severe than the vast majority of sentences meted out across the state for like offenses. (To be established at the hearing on this Application).
     
      
      . We note moreover that Mattheson asserts nothing more than conclusory allegations in support of his claim, insufficient for review in this court. Knighton, supra, at 1352.
     
      
      . Mattheson’s amended petition alleges:
      Petitioner’s Eighth and Fourteenth Amendment rights will be violated if his execution is allowed to proceed, notwithstanding the fact that Mr. Mattheson may well be insane; unable to understand the proceedings against him; or the reasons for his execution. (To be established at the hearing on this Application).
      Because we hold that we must defer to the state court’s determination that Mattheson is presently sane, we do not reach the issue whether the fifth and eighth amendments prohibit the execution of the mentally incompetent. Whether the Constitution provides such protection, and in what circumstances this constitutional right is triggered, are unresolved questions. See Solesbee v. Balkcom, 339 U.S. 9, 70 S.Ct. 457, 94 L.Ed. 604 (1950); Goode v. Wainwright, 731 F.2d 1482, 1483 (11th Cir.1984); Gray v. Lucas, 710 F.2d 1048, 1053-56 (5th Cir.), cert. denied, — U.S. -, 104 S.Ct. 211, 77 L.Ed.2d 1453 (1983).
     
      
      . Mattheson's amended petition alleges:
      Petitioner’s Eighth and Fourteenth Amendment rights have been violated because the death penalty is being administered in this case in a racially discriminatory manner, based solely on the race of the victim. To wit, the illegitimate factor of the race of the victim has a powerful effect on which defendants are sentenced to life imprisonment, and which are sentenced to death. As a result, when an offender is convicted of killing a white victim, he has a substantially greater likelihood of receiving the death penalty than an offender convicted of killing a black victim under otherwise identical circumstances. (To be established at the hearing on this Application).
     