KING, Circuit Judge:
Edward R. Byrne, Jr., a state prisoner under a sentence of death, moves this court for a certificate of probable cause to appeal the district court’s denial of his petition for a writ of habeas corpus. In addition, the state of Louisiana asks us to vacate the stay of execution granted by the district court. Finding that Byrne has failed to make a substantial showing of the denial of a federal right, we deny his application for a certificate of probable cause. Moreover, as Byrne has demonstrated neither a substantial case on the merits nor that the balance of the equities weighs in his favor, we vacate the stay of execution granted by the district court.
[504]*504I.
On the afternoon of August 14,1984, the body of Roberta Johnson (“Johnson”) was discovered in the locked office of a gas station in Bossier City, Louisiana. Three weeks later, the grand jury of Bossier Parish, Louisiana returned a true bill indicting Edward R. Byrne, Jr. (“Byrne”) for first degree murder in violation of La.Rev.Stat. Ann. § 14:30 (West 1986).1 M. Randal Fish (“Fish”) and Ford E. Stinson, Jr. (“Stin-son”) were appointed to represent Byrne at trial. On November 27, 1984, a twelve person jury found Byrne guilty as charged.2 In the penalty phase of Byrne’s bifurcated trial, the jury unanimously recommended the death penalty, finding the existence of three aggravating circumstances: (1) the victim had been killed during the commission of an armed robbery; (2) the offense was committed in a particularly heinous, atrocious and cruel manner; and (3) the victim was a witness to a crime committed by the defendant.3 See La.Code Crim.Proc.Ann. art. 905.4 (West 1984). Byrne was sentenced to death on January 29, 1984. Byrne’s conviction and sentence were upheld by the Louisiana Supreme Court, State v. Byrne, 483 So.2d 564 (La.1986), and his petition for rehearing was denied on March 7, 1986. Byrne’s petition for writ of certiorari to the United States Supreme Court was denied on October 6, 1986, Byrne v. Louisiana, — U.S. -, 107 S.Ct. 243, 93 L.Ed.2d 608 (1986), and Byrne’s petition for a rehearing of that decision was denied on December 1, 1986.
Byrne’s subsequent attempt to secure post-conviction relief in the Louisiana state courts proved unsuccessful. Having exhausted his state remedies, Byrne filed a “Petition for Writ of Habeas Corpus, Request For Evidentiary Hearing, And Application For A Stay of Execution” in the United States District Court for the Western District of Louisiana on January 16, 1987. On January 17, the district court granted Byrne a stay of execution, requested all records and transcripts, ordered that briefs be filed, and granted Byrne’s application to proceed in forma pauperis. In a memorandum ruling filed August 31, the district court, after concluding that an evi-dentiary hearing was unwarranted, denied Byrne’s habeas petition and found that “[a]ll of [Byrne’s] allegations have been conclusory, unsubstantiated and clearly refuted by the existing record.” The district court also entered a separate judgment denying Byrne’s petition. On September 17, the district court entered a supplemental order to clarify its earlier ruling. In that supplemental order, the district court stressed that the January 17 stay of execution would remain in effect until all appeals concerning Byrne’s application for habeas relief were either waived or exhausted. On September 24, the district court denied Byrne’s Rule 60(b) motion for relief from the judgment.
[505]*505Byrne filed timely notice of appeal from the denial of habeas relief and sought a certificate of probable cause to authorize appeal and permission to proceed in forma pauperis.4 On October 5, the district court found that a certificate of probable cause should not issue and denied Byrne’s application “as frivolous, without merit and not being in good faith.” We have before us Byrne’s application for a certificate of probable cause to appeal. In addition, the state requests that we vacate the district court’s stay of execution.
II.
In his application, Byrne argues that: (1) the district court erred by failing to conduct an evidentiary hearing to determine (a) whether the trial court violated Byrne’s rights to a fair trial and impartial jury by improperly restricting defense voir dire on the meaning of life imprisonment; (b) whether erroneous and misleading statements by the state prosecutor during voir dire regarding the potential for future release on parole improperly influenced the jury; and (c) whether judicial misconduct prevented Byrne from presenting evidence on the issue of the effect the “tainted” voir dire had on the jury; (2) the state prosecutor’s improper comments concerning Johnson’s character rendered Byrne’s trial fundamentally unfair; (3) the district court erred by failing to conduct an evidentiary hearing on Byrne’s claims that his attorneys accorded him ineffective representation both at trial and on direct appeal; (4) because the jury was allowed to consider an impermissible aggravating circumstance, a new sentencing hearing is required; and (5) relevant mitigating evidence was excluded at the penalty phase of the trial in violation of the principles set forth by the Supreme Court in Skipper v. South Carolina, 476 U.S. 1, 106 S.Ct. 1669, 90 L.Ed.2d 1 (1986) and similar cases.
III.
The standard for granting a certificate of probable cause under Federal Rule of Appellate Procedure 22(b) is whether the petitioner has made a substantial showing of a denial of a federal right. Brogdon v. Butler, 824 F.2d 338, 340 (5th Cir.), cert. denied, — U.S. -, 108 S.Ct. 13, 97 L.Ed.2d 802 (1987) (citing Stewart v. Beto, 454 F.2d 268, 279 n. 2 (5th Cir.1971)). In requiring a substantial showing of the denial of a federal right, the petitioner need not show that he should prevail on the merits. Barefoot v. Estelle, 463 U.S. 880, 893 n. 4, 103 S.Ct. 3383, 3394 n. 4, 77 L.Ed.2d 1090 (1982) (quoting Gordon v. Willis, 516 F.Supp. 911, 913 (N.D.Ga.1980)). Rather, he must demonstrate that the issues are subject to debate among jurists of reason; that a court could resolve the issues in a different manner; or that the questions are worthy of encouragement to proceed further. Id. “In a capital case, the nature of the penalty is a proper consideration in determining whether to issue a certificate of probable cause, but the severity of the penalty does not in itself suffice to warrant the automatic issuing of a certificate.” Barefoot, 463 U.S. at 893, 103 S.Ct. at 3395. While we are acutely aware of the fact that Byrne faces a sentence of execution, we are unable to conclude that Byrne has made a substantial showing of the denial of a federal right. Therefore, we deny his application for a certificate of probable cause to appeal.
IV.
A. Voir Dire
In his opening statements during voir dire, Fish described the sentencing alternatives available to the jury in a manner designed to favorably predispose them towards a sentence of life imprisonment. Fish sought to impress upon the veniremen the notion that life imprisonment would not result in any form of early release. The following exchange occurred between Fish, the state prosecutor, and the trial court:
[MR. FISH:] ... But there are only two choices. One is life imprisonment without benefit of parole, probation or [506]*506suspension of sentence. That means life in prison with no parole; it means the parole board can’t let him out. No probation — that means the Judge can’t put him on probation. No suspension of sentence. That means the Judge can’t suspend his sentence.
MR. BROWN: Your Honor, my only objection is that that is not an entirely accurate statement of the law. I don’t object to him stating what the penalties are, but as far as his comment about what the parole board may or may not can do, I think it’s not entirely accurate, but—
MR. FISH: Your Honor, I think without parole, it certainly means the parole board can’t let him out.
MR. BROWN: Mr. Fish knows full well what that means and what the possibilities are. And I object to that particular statement.
MR. FISH: Your Honor, I would — I would—
THE COURT: I’m going to sustain the objection and I would admonish those of you who are in the jury box and those of you who are prospective jurors that what the attorneys say about the law may or may not be the law. The law in this case will be given to you at the close of this case by the Court and it will be your duty to accept that law as given by the Court irregardless [sic] of what the attorneys may or may not say.
MR. FISH: Your Honor, I would move for a mistrial on the basis of Mr. Brown’s statement. I think that it’s improper for Mr. Brown to raise the element of a possibility of release when dealing with a death penalty case.
MR. BROWN: I have no [sic] raised that possibility at all, Your Honor. I mean I, — stayed away from it.
THE COURT: You made a valid objection; the Court sustained the objection. The request for mistrial is denied.
Later, while questioning prospective jurors, Fish once again stated that the parole board was powerless to grant parole to a person sentenced to life imprisonment. Once again, the state prosecutor objected. This time, however, the trial court overruled the objection but warned Fish that he might be opening the door for the state to go into the consequences of life imprisonment. At that point, the state prosecutor stressed that he was “trying to avoid that because [he knew] the danger of it ... and that’s why [he objected].” The trial court once again admonished the jury to disregard the attorneys’ depiction of the law and to concentrate instead on the law as given to them by the trial court. The Louisiana Supreme Court held that the state prosecutor’s objections “were not necessarily well founded” since Fish’s statements were merely incomplete rather than inaccurate. Byrne, 483 So.2d at 570.5
Byrne contends that the district court erred by failing to hold an evidentiary hearing on Byrne’s claims that the voir dire was constitutionally improper. “[T]o receive a federal evidentiary hearing, a petitioner must allege facts that, if proved, would entitle him to relief.” Wilson v. Butler, 825 F.2d 879, 880 (5th Cir.1987), cert. denied, — U.S. -, 108 S.Ct. 1059, 98 S.Ct. 1021 (1988). This requirement not only avoids wasting already overburdened federal judicial resources, but also reduces federal-state tensions in cases where a federal hearing would serve no good purpose. Id. Applying this requirement, we find no error in the district court’s refusal to conduct an evidentiary hearing. Byrne’s claims are clearly without merit as to matters of both fact and law, and he has failed to allege or demonstrate the existence of facts which would entitle him to relief.
As an initial matter, Byrne argues that under King v. Lynaugh, 828 F.2d 257, reh’g en banc granted, 828 F.2d 269 (5th [507]*507Cir.1987), the trial court’s “restriction” of his right to inquire into the veniremen’s understanding of life imprisonment and parole violated his constitutional rights to a fair trial and an impartial jury. Byrne’s argument is of no moment. First, as we have stressed, “[t]he grant of a rehearing en banc vacates the panel opinion, which thereafter has no force.” Selvage v. Lynaugh, 842 F.2d 89, 91 (5th Cir.1988). Byrne’s reliance on King, therefore, is misplaced.
In Selvage, we noted that the legal basis for the argument that one can be denied a constitutional right to inquire into the veniremen’s understanding of parole “enjoyed virtually no support in this circuit before the panel opinion in King v. Lynaugh. ” Id. We went on to conclude that “the inquiry into parole matters in the selection of a jury cannot be required so long as the state may instruct the selected jury that it cannot consider the subject at all.” Id. at 92. Therefore, we held that “in the face of our controlling cases we cannot conclude that refusing to examine veniremen about their understanding of parole or their understanding of a life sentence, a subject they will later be told they are not to consider at all, denied Selvage any right secured by the Constitution.” Id.
While Selvage was decided with reference to Texas law, its reasoning is equally appropriate in the instant case. Under Louisiana law, “[t]he conditions under which a person sentenced to life imprisonment without the benefit of parole, probation, or suspension of sentence can be released in the future are not a proper consideration for a capital sentencing jury, and shall not be discussed in the jury’s presence.” Byrne, 483 So.2d at 570 (citing cases). This prohibition extends to voir dire as well as to the sentencing phase of a capital case. Id. An evidentiary hearing on Byrne’s contention, therefore, would be futile.6
Byrne also contends that an evidentiary hearing is necessary to determine whether the state prosecutor’s objections and the trial court’s rulings during voir dire deprived the sentencing process of the reliability required by the eighth amendment. Relying on Gardner v. Florida, 430 U.S. 349, 97 S.Ct. 1197, 51 L.Ed.2d 393 (1977), and Caldwell v. Mississippi, 472 U.S. 320, 105 S.Ct. 2633, 86 L.Ed.2d 231 (1985), Byrne argues that there is an unacceptable risk that the sentencing determination was improperly based on inaccurate or erroneous information.
“Our review of the propriety of prosecutorial comments made during a state triai is ‘the narrow one of due process and not the broad exercise of supervisory power that [we] would possess in regard to [our] own trial court.’ ” Willie v. Maggio, 737 F.2d 1372, 1390 (5th Cir.1984) (quoting Donnelly v. DeChristoforo, 416 U.S. 637, 642, 94 S.Ct. 1868, 1871, 40 L.Ed.2d 431 (1974)). As a general rule, therefore, “[i]n federal habeas actions, improper jury argument by the state does not present a claim of constitutional magnitude unless it is so prejudicial that the petitioner’s state court trial was rendered fundamentally unfair within the meaning of the Fourteenth Amendment’s Due Process clause.” Felde v. Blackburn, 795 F.2d 400, 403 (5th Cir. 1986), cert. denied, — U.S. -, 108 S.Ct. 210, 98 L.Ed.2d 161 (1987); see also Don-[508]*508nelly, 416 U.S. at 645, 94 S.Ct. at 1872. To establish that a prosecutor’s remarks are so inflammatory as to have prejudiced the substantial rights of a defendant, a habeas petitioner must demonstrate either persistent and pronounced misconduct or that the evidence was so insubstantial that absent the remarks, a conviction would probably not have occurred. Bridge v. Lynaugh, 838 F.2d 770, 774 (5th Cir.1988); Felde, 795 F.2d at 403. The requisite showing is a difficult one and Byrne falls far short of demonstrating a violation which impinged on his constitutional right to a fundamentally fair trial. See Ortega v. McCotter, 808 F.2d 406, 407 (5th Cir.1987).
Any inference of future release which could be gleaned by the jury from the complained-of exchange would be tenuous at best. The state prosecutor did not directly interject the notion of pardon or commutation of sentence into the proceedings; rather, the only explicit reference to future release came from Fish in his motion for a mistrial. Moreover, as is clear from the record, the state prosecutor, recognizing the danger of injecting arbitrary factors— such as the specter of future release — into the sentencing process, sought merely to prevent Fish from delivering what the state prosecutor perceived to be an inaccurate monologue on the meaning of life imprisonment. That attempt was ultimately unsuccessful since the trial court overruled the second objection and, while admonishing Fish that he might be opening a Pandora’s box with his comments, allowed Fish to continue to emphasize the irrevocable nature of a life imprisonment sentence. Notably, each of the state prosecutor’s objections was immediately followed by the trial court’s admonition that the statements of the attorneys were not the law, and that the jury was obligated to apply the law as provided by the trial court at the close of trial. Throughout the trial, the jurors were reminded that the statements and arguments of the attorneys were not evidence. Finally, the trial court properly instructed the jury that the alternative to death was “life imprisonment without the benefit of probation, parole or suspension of sentence.” 7
Our conclusion that the allegedly “tainted” voir dire did not constitutionally impair the sentencing process is buttressed by the stark contrasts between the facts in the cases relied upon by Byrne and those before us here. In Gardner, for example, the petitioner was convicted of first degree murder in a Florida court and, after the required sentencing hearing, the jury advised the trial court to impose a life sentence on the ground that the statutory mitigating circumstances outweighed the statutory aggravating circumstances. The trial judge, however, relying in part on a presen-tence investigation report that he had ordered — portions of which were neither disclosed to nor requested by counsel for the parties — imposed a death sentence. The Supreme Court held that the petitioner “was denied due process of law when the death sentence was imposed, at least in part, on the basis of information which [the defense] had no opportunity to deny or explain.” Gardner, 430 U.S. at 362, 97 S.Ct. at 1207.
In the instant case, despite Byrne’s assertions to the contrary, his counsel was repeatedly permitted to explore before the jury the meaning of life imprisonment. These remarks were not countered by contrary arguments from the state prosecutor. Moreover, the trial court properly instructed the jury that the alternative to death [509]*509was life imprisonment without benefit of probation, parole or commutation of sentence. Gardner, therefore, is inapposite to the case at bar.
Byrne’s reliance on Caldwell is even more misplaced. Caldwell involved comments made by the prosecutor during the sentencing phase of trial to the effect that the jury’s decision as to life or death was not final, that the decision would be automatically reviewable and that the jury should not be made to feel as if the entire burden for the defendant’s life rested with them. The Supreme Court held that such comments “ ‘presen[t] an intolerable danger that the jury will in fact choose to minimize the importance of its role,’ a view that would be fundamentally incompatible with the Eighth Amendment requirement that the jury make an individualized decision that death is the appropriate punishment in a specific ease.” Darden v. Wainwright, 477 U.S. 168, 183 n. 15, 106 S.Ct. 2464, 2473, n. 15, 91 L.Ed.2d 144 (quoting Caldwell, 472 U.S. at 333, 105 S.Ct. at 2642).
Caldwell is readily distinguishable from the case at bar. The comments in Caldwell were made at the sentencing phase of trial and were explicitly approved by the trial judge. In the instant case, the objections and rulings were made during voir dire, “greatly reducing the chance that they had any effect at all on sentencing.” See Darden, 477 U.S. at 183 n. 15, 106
S.Ct. at 2473 n. 15. Moreover, in the instant case, the trial court overruled one of the two objections by the state prosecutor, repeatedly instructed the jurors that the attorneys’ arguments may or may not be accurate reflections of the law and consistently exhorted them to apply the law only as given them by the trial court. Finally, as noted in Darden, “Caldwell is relevant only to certain types of comment — those that mislead the jury as to its role in the sentencing process in a way that allows the jury to feel less responsible than it should for the sentencing decision.” 477 U.S. at 184 n. 15, 106 S.Ct. at 2473 n. 15. Caldwell is simply not implicated in the case before us.
Byrne has failed to demonstrate that the record is in any way inadequate to dispose of his meritless claim that the events which transpired during voir dire deprived his sentence of the reliability demanded by the eighth amendment. On the contrary, our review of the record leads us, as it did the Louisiana Supreme Court, to the ineluctable conclusion that “in the context of the entire record, the prosecutor’s objections to defense counsel’s statements neither deflected the jury’s attention from the ultimate significance and finality of the penalty recommendation nor misguided the jury’s sentencing discretion by introducing arbitrary factors.” See State v. Byrne, 483 So.2d at 571.8
[510]*510
B. Comments on Victim’s Character
Byrne complains that several comments by the state prosecutor constituted improper references to Johnson’s character and the impact of the crime on family members, as condemned by the Supreme Court in Booth v. Maryland, — U.S. -, -, 107 S.Ct. 2529, 2533, 96 L.Ed.2d 440 (1987). Specifically, Byrne objects to the following remarks by the state prosecutor:
She [Johnson] was a big girl. She was twenty-five years of age. Her mother died when she was seventeen and her father died shortly after her funeral. So neither of them will be here to testify. * # * * # #
I’m telling you, this case is a lot more than just an armed robbery and murder. He knew what she did. He knew how much money she handled. And he went with her for one reason — to steal from her_And he set her up. She fell in love with him. She loved him.
* * # * # *
Did he care for Robbie Johson [sic]? Think about Robbie Johnson’s feelings. She’s a big part of this trial. Don’t forget about her. What kind of a girl was Robbie Johnson compared to this man over here. You know what kind of man he is. What kind of girl was Robbie Johnson?
* * # * * *
Robbie — steady employee — in May of this year promoted to manager of the Racetrack Station where she’d worked since 1982. Her mother died when she was 17. He [sic] father died in October of this year, after she was buried. They can’t be here today. Dependable. A good decent girl who loved this man.
In Booth, the Supreme Court held that a Maryland statute requiring the introduction of a “victim impact statement” (“VIS”) at the sentencing phase of a capital murder trial violated the eighth amendment. The information in the VIS at issue in Booth, which could either be read to the jury or testified to by family members, described in pronounced detail the personal characteristics of the victims, the emotional impact of the crime on the family, and the family members’ opinions and characterizations of the crime and the defendant. After analyzing the many dangers inherent in allowing such information before the jury, the Supreme Court “rejected] the contention that the presence or absence of emotional distress of the victim’s family, or the victim’s personal characteristics, are proper sentencing considerations in a capi[511]*511tal case.” Booth, 107 S.Ct. at 2535. The Supreme Court strongly disapproved of the notion that the sentencing decision might properly “turn on the perception that the victim was a sterling member of the community rather than someone of questionable character.” Id. at 2534. “Of course, our system of justice does not tolerate such distinctions.” Id. at 2534 n. 6.
The Supreme Court was careful to stress that its disapproval of victim impact information at the sentencing phase of a capital trial does not mean that information about the impact of the crime on the family and the victim’s personal characteristics will never be relevant in any context. Booth, 107 S.Ct. at 2535 n. 10. “Similar types of information may well be admissable because they relate directly to the circumstances of the crime.” Id. This exception to Booth’s general admonishments is sufficient to cover the prosecutor’s references to Byrne’s “setting up” the woman who loved him. That information related to the circumstances of the case and was supported by the evidence. Other references to the fact that Byrne used people or did not care about others would fall within the same category. We are left, therefore, with several oblique references to Johnson’s family and the state prosecutor’s description of Johnson as a caring and decent individual.
While Booth did not discuss the issue, it seems clear that even if the state prosecutor’s brief references to Johnson’s character and family were improper,9 we must still determine, under the teachings of Donnelly and Darden, whether they rendered Byrne’s trial fundamentally unfair so as to invite habeas relief. Booth involved much more than improper arguments by the prosecutor. Even a cursory comparison of the VIS permitted before the jury in Booth and the comments of the prosecutor in the instant case reveals a wealth of difference in the scope, tone and effect of the information provided. The introduction of the VIS in Booth, much as the prosecutor’s references to appellate review and the role of the jury in Caldwell, clearly created an unacceptable risk that the eighth amendment’s requirement of heightened reliability in capital sentencing determinations had been compromised. In both Booth and Caldwell, the improper statements or comments were focused, unambiguous and strong, and the information imparted to the jury received a seal of approval from the trial court.
The same cannot be said of the instant case. The state prosecutor’s allegedly improper remarks were brief and, with respect to the references to Johnson's family, cryptic. The information divulged in the remarks — that Johnson, a heavy-set young woman, was a steady, decent and dependable employee — was already before the jury, in large measure, because of testimony during the guilt phase establishing Johnson’s innocence of any wrongdoing. Finally, and most importantly, the trial court not only admonished the jury that they were “not to be influenced by sympathy, passion or prejudice,” but also properly instructed them that it was their “duty to consider the circumstances of the offense, the character and propensities of the defendant in determining the sentence to be imposed.” Moreover, the jury was instructed at the close of the guilt phase that the attorneys’ arguments were not evidence. Far from requiring the jury to consider the character of the victim and the impact on the victim’s family, the trial court directed the jury’s attention to the defendant and his crime, and instructed them to ignore any plays for sympathy from the state prosecutor. While we refuse to hold that prosecutorial references to a victim’s character or family [512]*512can never render a trial fundamentally unfair, we conclude that under the facts of the instant case, the state prosecutor’s comments did not rise to the level of a constitutional violation cognizable in habe-as.
C. Ineffective Assistance of Counsel
Byrne asserts that an evidentiary hearing is necessary to evaluate his various claims of ineffective assistance of counsel. The question of whether an evidentiary hearing is necessary to resolve a charge of inadequate representation turns on an assessment of the record. If the petitioner’s allegations cannot be resolved absent an examination of evidence beyond the record, a hearing is required, Clark v. Blackburn, 619 F.2d 431, 432 (5th Cir.1980); if the record is clearly adequate to fairly dispose of the claims of inadequate representation, further inquiry is unnecessary, Baldwin v. Maggio, 704 F.2d 1325, 1329 (5th Cir.1988), cert. denied, 467 U.S. 1220, 104 S.Ct. 2669, 81 L.Ed.2d 374 (1984); see also Joseph v. Butler, 838 F.2d 786, 788 (5th Cir.1988). After reviewing the record, we agree with the district court that Byrne’s claims may be resolved without recourse to an eviden-tiary hearing.
Byrne’s claims of ineffective assistance of counsel must be evaluated under the two-pronged test enunciated by the Supreme Court in Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). The test requires first, “a showing that counsel made errors so serious that counsel was not functioning as the ‘counsel’ guaranteed by the Sixth Amendment,” and second, a showing that the deficient performance so prejudiced the defense that the defendant was deprived of a fair and reliable trial. Uresti v. Lynaugh, 821 F.2d 1099, 1101 (5th Cir.1987) (quoting Strickland, 466 U.S. at 687, 104 S.Ct. at 2064). Strickland imposes a severe burden on a defendant. Procter v. Butler, 831 F.2d 1251, 1255 (5th Cir.1987). With respect to the deficiency prong, for example, the defendant must demonstrate that counsel’s representation fell below an objective standard of reasonableness as measured by prevailing professional standards. Martin v. McCotter, 796 F.2d 813, 816 (5th Cir.1986), cert. denied, — U.S. -, 107 S.Ct. 935, 93 L.Ed.2d 985 (1987). We have stressed that “great deference is given to counsel, ‘strongly presuming that counsel has exercised reasonable professional judgment.’ ” Martin, 796 F.2d at 816 (quoting Lockhart v. McCotter, 782 F.2d 1275, 1279 (5th Cir.1986), cert. denied, — U.S. -, 107 S.Ct. 873, 93 L.Ed.2d 827 (1987)).
In evaluating whether the defendant was prejudiced by counsel’s allegedly incompetent performance, “[i]t is not enough for the defendant to show that the errors had some conceivable effect on the outcome of the proceeding.” Strickland, 466 U.S. at 693, 104 S.Ct. at 2067. Rather, the defendant must demonstrate “a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different. A reasonable probability is a probability sufficient to undermine confidence in the outcome.” Id. at 694, 104 S.Ct. at 2068. Strickland requires that the defendant affirmatively prove prejudice. Czere v. Butler, 833 F.2d 59, 64 (5th Cir.1987). As Strickland also authorizes us to proceed directly to the question of prejudice, if Byrne fails to demonstrate prejudice, the alleged deficiencies in the attorneys’ performance need not even be considered. See Strickland, 466 U.S. at 698-99, 104 S.Ct. at 2070; Schwander v. Blackburn, 750 F.2d 494, 502 (5th Cir.1984).
Byrne first complains that his attorneys failed to have him evaluated by a mental health professional. The trial court noted that Byrne “refused to cooperate in his own defense, asked to be executed, showed no remorse for his actions, laughed during the guilt and sentencing phases of his trial and ridiculed his family and attorneys for their concern.” Based on these observations, Byrne argues that his trial attorneys were ineffective for failing to discover evidence of his underlying mental disorder and for not presenting that evidence both at the guilt and sentencing [513]*513stages of his trial.10
We will assume, for the sake of argument, that Byrne was in fact suffering from a mental disorder and that such evidence might well have been relevant both as to competency and mitigation. Byrne must still demonstrate, however, that his attorneys had some indication that mental impairment might prove a promising line of defense. See Wilson v. Butler, 813 F.2d 664, 671 (5th Cir.1987); see also James v. Butler, 827 F.2d 1006, 1017 (5th Cir.1987) (where defendant did not advise counsel of possible defense centering on the impairment of mental faculties due to drugs, counsel’s pursuance of different line of defense was not unreasonable). Byrne does not allege that he intimated to his attorneys that he was suffering from a mental disorder. Moreover, neither Byrne’s actions following the arrest nor his testimony at the guilt stage of trial gave any hint of a problem. Similarly, the testimony of Byrne’s father, mother, sister and brother was empty of any reference to psychological difficulties. The record, therefore, fails to provide any indication that a psychiatric evaluation was warranted. Indeed, overwhelming evidence of the calculated nature of Byrne’s crime — a crime planned and committed for pecuniary gain rather than out of passion — belies any such notice. Nevertheless, Byrne argues that the trial court’s observations of Byrne’s behavior demonstrate that there were indications of an underlying mental disorder sufficient to prompt further investigation by competent counsel. As the district court was quick to point out, however, the behavior noted by the trial court would be equally consistent with the behavior of a callous individual with little or no remorse for his crimes. We cannot conclude, therefore, that Byrne has demonstrated any indication that his attorneys were alerted — or should have been alerted — to the presence of an underlying mental disorder.
Byrne also asserts that his attorneys were ineffective because they did not move to suppress the fruits of what Byrne now characterizes as an “illegal warrantless arrest.” The district court found that Byrne “[did] not come forward with one shred of evidence or basis in the record to prove that the arrest was, in fact, illegal or that his attorney was aware of facts that warranted a further investigation.” As the Supreme Court has held:
Where defense counsel’s failure to litigate a Fourth Amendment claim competently is the principal allegation of ineffectiveness, the defendant must also prove that his Fourth Amendment claim is meritorious and that there is a reasonable probability that the verdict would have been different absent the excluda-ble evidence in order to demonstrate actual prejudice.
Kimmelman v. Morrison, 477 U.S. 365, 106 S.Ct. 2574, 2583, 91 L.Ed.2d 305 (1986). Byrne argues that if given the opportunity to present evidence at a hearing, he could demonstrate that the arresting officers were acting without a warrant. It is clear, however, that bold assertions on a critical issue in a habeas petition, unsupported and unsupportable by anything else contained in the record, are insufficient to warrant an evidentiary hearing. See Joseph, 838 F.2d at 788 (quoting Ross v. Estelle, 644 F.2d 1008, 1011 (5th Cir.1983) (per curiam)).
The record contradicts Byrne’s allegations. Officer Harry James of the Lees-ville Police Department, one of the officers who arrested Byrne, testified that prior to the arrest, he had a warrant number from Bossier City for Byrne’s arrest. In addition, Detective Sergeant George West of [514]*514the Bossier City Police Department testified that after conducting an investigation of the circumstances surrounding Johnson’s murder, he had obtained a warrant for Byrne’s arrest. While the warrant itself does not appear in the record, there are no indications that the testimony of the officers was either inaccurate or perjured. Therefore, Byrne’s conclusory allegations to the contrary are of no moment.
Finally, Byrne argues that the inculpato-ry statements he made to police were prompted by improper police promises of leniency and, therefore, were involuntary. Specifically, Byrne claims that “Detective West told [Byrne] that he would get the death penalty if he did not confess, and conversely, that he would get a term of life imprisonment if he did.” This allegation enjoys no factual support in the record. A review of the testimony of the police officers involved in Byrne’s arrest and subsequent transportation to Bossier City— where Byrne delivered a taped confession —reveals that Byrne was advised of his constitutional rights and freely made the incriminating statements.11 Byrne’s con-clusory assertion to the contrary is not even supported by an affidavit chronicling his version of the circumstances surrounding the statements. Moreover, at trial, Fish informed the trial court that:
I made a determination after reviewing the statements of my client that they were made freely and voluntarily and I saw no reason to exclude the jury while the voluntariness of the statement was established outside their presence and then have to establish it again with their presence. Therefore I informed Mr. Brown that it would be all right with me if he just proceeded to lay the foundation for the statements. In other words, proof that it was given freely and voluntarily without retiring the jury.
Under the circumstances, we cannot conclude that Byrne’s conclusory allegations provide the slightest impetus for an eviden-tiary hearing.
D. Invalid Aggravating Circumstance
As noted earlier, the Louisiana Supreme Court found that one of the statutory aggravating circumstances found by the jury — that Johnson was an eyewitness to a crime committed by Byrne — was invalid because Johnson was not an eyewitness to an earlier, independent crime committed by Byrne. Byrne, 483 So.2d at 575. The Louisiana Supreme Court concluded, however, that the finding of the unproved aggravating circumstance did not inject an arbitrary factor into the sentencing proceeding as it rested upon otherwise admissable evidence properly adduced at the guilt stage. Id. at 576. Byrne now contends that he is entitled to a new sentencing hearing because the jury’s consideration of the invalid aggravating circumstance injected an arbitrary factor into the sentencing proceeding. Byrne’s argument must fail, however, for “[t]he fact that an invalid [515]*515statutory aggravating circumstance has been found does not constitutionally impair a death sentence under the Louisiana procedure where the jury has also found another aggravating circumstance which is supported by the evidence and is valid under the law and of itself suffices to authorize the imposition of the death penalty.” James, 827 F.2d at 1013 (citing cases).
The armed robbery aggravating circumstance was clearly supported by the evidence. As the Louisiana Supreme Court noted:
The evidence fully supports the jury’s finding that Roberta Johnson died during the commission of an armed robbery. The defendant admitted that he administered the fatal blows during the robbery of Roberta. On the witness stand, defendant gave a more detailed account of the robbery. Police recovered $6,962.25 of the $7,686.60 taken from the Racetrack Service Station from defendant’s motel room.
Byrne, 483 So.2d at 576. “That court’s determination is entitled to great weight in our review.” Wingo v. Blackburn, 786 F.2d 654, 655 (5th Cir.1986), cert. denied, — U.S. -, 107 S.Ct. 1984, 95 L.Ed.2d 823 (1987). This aggravating circumstance alone was sufficient to authorize the imposition of the death penalty and there has been no legitimate challenge to its legal validity in this case.12 Byrne’s death sentence, therefore, was not constitutionally impaired by the jury’s finding of an invalid aggravating circumstance.13 See James, 827 F.2d at 1012-13; see also Zant v. Stephens, 462 U.S. 862, 875-89, 103 S.Ct. 2733, 2741-44, 77 L.Ed.2d 235 (1983); Celestine v. Butler, 823 F.2d 74, 78 (5th Cir.), cert. denied, — U.S. -, 108 S.Ct. 6, 97 L.Ed.2d 796 (1987).
E. Exclusion of Mitigating Evidence
Byrne, relying on Skipper for the proposition that the sentencer may not be precluded from considering any relevant mitigating evidence, argues that mitigating evidence was impermissibly kept from the [516]*516jury in the instant case. First, Byrne claims that Fish and Stinson failed “to secure documents from the United States’ Army to mitigate allegations of his court martial and secure evidence concerning [Byrne’s] mental condition.” Next, Byrne complains that Fish and Stinson failed to lay a proper foundation for the evidence they did have concerning Byrne’s military record. Finally, Byrne faults Fish and Stinson for failing to contest the trial court’s ruling excluding this evidence on appeal.
At the guilt stage of trial, Byrne testified that he was honorably discharged from the Army and remained on inactive reserve. Byrne also explained that while he was in the Army, he was arrested for criminal damage to property and disturbing the peace in connection with his tossing a tear gas grenade into a motorcycle club. Apparently, Byrne was also charged with possession of marijuana while in the Army. Byrne testified that none of the offenses he had committed was a felony.
At the sentencing stage, counsel for Byrne called Byrne’s father to testify. Byrne’s father testified generally as to Byrne’s service in the military and specifically as to a military commendation received by Byrne. In addition, Byrne’s father testified that a letter from Byrne’s commander and the commendation showed that his son “did an exceptionally good job” and received an honorable discharge. During cross-examination, the state prosecutor questioned Byrne’s father about several less than savory aspects of his son’s military career. In particular, the state prosecutor sought to elicit information concerning Byrne’s court martial in Korea for being absent without leave (“AWOL”) for approximately four days. Byrne’s father, however, managed to explain that one can be charged with AWOL for being gone for as short as a few hours and, on re-direct examination, Byrne’s father testified that AWOL charges were not an unusual occurrence in the military. He also agreed that even servicemen who had been in “a number of serious AWOLS” could receive honorable discharges. Moreover, Byrne’s father testified that a summary court martial —such as the one Byrne received in Louisiana for being AWOL — was less serious than a regular court martial.
Later, the state prosecutor attempted to introduce a certified copy of what purported to be Byrne’s military records. Stinson objected to the introduction of the records on the grounds that “[t]hey’ve not been properly identified and there’s been no foundation laid for their introduction.” As the military person who allegedly certified the records was not called to testify as to the identity of the documents, the trial court sustained Stinson’s objection. In addition, however, the trial court refused to allow Stinson to introduce Byrne’s commendations into evidence on the same ground.
In his closing argument, the state prosecutor made a brief reference to Byrne’s troubles in the Army:
We learned from him when he testified the first part of the trial that he had some criminal convictions, minor convictions — carrying a concealed weapon; disturbing the peace; criminal property damage. I believe he said when he got out of the military he had been court martialed for marijuana possession. Court martialed for AWOL. And some other problems before he went into the military. This is not a significant prior criminal history. But it’s also not an insignificant prior criminal history.
In response, Stinson painted a rosier picture of Byrne’s service to his country:
Other mitigating circumstances: you know that Edward at the age of eighteen joined the Army. He served his country. He hasn’t fought in a war, anything like that, but he joined the Army, served in the Army. Served overseas in Korea in the Army. He did have a problem. He was absent without leave, but the end result was he was honorably discharged from the United States Army. There’s a lot of people that can’t say that about themselves.
In rebuttal, the prosecutor made a single reference to the “minor” troubles Byrne had been in and, in what could be construed [517]*517as a subtle aside, told the jury that “[w]e can’t go AWOL on our duties.”
There is no disputing that the Supreme Court’s decisions in Lockett v. Ohio, 438 U.S. 586, 604, 98 S.Ct. 2954, 2964, 57 L.Ed.2d 973 (1978), and Eddings v. Oklahoma, 455 U.S. 104, 110, 102 S.Ct. 869, 874, 71 L.Ed.2d 1 (1982), require that the sentencer in a capital case not be precluded from considering, as a mitigating factor, any aspect of a defendant’s character or record. Skipper, 106 S.Ct. at 1670-71. “Equally clear is the corollary rule that the sentencer may not refuse to consider or be precluded from considering ‘any relevant migi-tating evidence.’ ” Id. at 1671 (quoting Eddings, 455 U.S. at 114, 102 S.Ct. at 877); see also Hitchcock v. Dugger, — U.S. -,-, 107 S.Ct. 1821, 1824, 95 L.Ed.2d 347 (1987). For several reasons, however, we find that Byrne has failed to raise a colorable constitutional claim on this issue.
With respect to Byrne’s charge that his attorneys failed to secure mitigating evidence about his court martials, the district court correctly noted that “Byrne does not specify which evidence should have been proffered concerning his military record; thus, it cannot be determined whether the evidence would have likely affected the outcome of the penalty phase.” Indeed, given the fact that Stinson successfully objected to the state prosecutor’s attempt to introduce into evidence what purported to be Byrne’s military records, it would be logical to assume that the prejudicial impact of drawing further attention to Byrne’s military record may well have outweighed any mitigating benefit. As it was, the jury was only confronted by several brief references to Byrne’s troubles in the military — all of which were explained away by either Byrne or his father through testimony. Byrne has failed to concretely allege the existence of specific mitigating evidence which his attorneys should have secured.
Next, Byrne argues that his attorneys should have appealed the trial court’s exclusion of evidence of the alleged certificate and letter given to Byrne by the military. Byrne argues that since these documents constituted relevant, mitigating evidence, their exclusion was improper under Skipper. Byrne does not contest the fact, however, that his trial counsel failed to properly identify the documents and did not lay a proper foundation before attempting to introduce the documents. As a result, the trial court’s action did not fall within the ambit of Skipper.14 Byrne’s attorneys’ failure to raise the argument on appeal, therefore, did not constitute ineffective assistance of counsel.
This brings us to the heart of the matter; was Byrne accorded constitutionally ineffective assistance of counsel due to his attorneys’ failure to lay a proper foundation for introducing the purported award certificate and letter from Byrne’s commanding officer? We must answer that query in the negative. In order to lay a proper foundation, Byrne’s attorneys would presumably have had to call someone from the military to testify. Had a military witness taken the stand in order to allow counsel to get the mitigating military documents into evidence, it is equally conceivable that Byrne’s military records could then have been successfully entered as well. As Byrne’s attorneys sought to keep Byrne’s military records — which included, presumably, some specific information about his court martials and arrests — away from the jury, the decision not to call a military witness would appear to be a tactical decision.
Even assuming that Byrne’s attorneys were unreasonably deficient in failing to get the documents into evidence, Byrne has failed to demonstrate that he was preju[518]*518diced as a result. As the Supreme Court has stated:
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, 466 U.S. at 695, 104 S.Ct. at 2068-69. In the instant case, Byrne’s father testified briefly about the contents of the documents and the jury was repeatedly informed that Byrne received an honorable discharge and that his crimes were insignificant or minor. Similarly, the state prosecutor failed to emphasize Byrne’s military problems in closing arguments. While we do not conclude that an attorney’s failure to assure the introduction of certain mitigating evidence could never constitute ineffective representation, we find that in the instant case, Byrne has failed to meet the serious burden imposed on him by Strickland. 15
V.
Our standard for review of a stay of execution is essentially the same as the measure for granting a stay. Selvage, 842 F.2d at 91. Generally, we must consider:
(1) whether the movant has made a showing of likelihood of success on the merits, (2) whether the movant has made a showing of irreparable injury if the stay is not granted, (3) whether the granting of the stay would substantially harm the other parties, and (4) whether the granting of the stay would serve the public interest.
O’Bryan v. McKaskle, 729 F.2d 991, 993 (5th Cir.1984); O’Bryan v. Estelle, 691 F.2d 706, 708 (5th Cir.1982), cert. denied, 465 U.S. 1013, 104 S.Ct. 1015, 79 L.Ed.2d 245 (1984); Ruiz v. Estelle, 666 F.2d 854, 856 (5th Cir.1982).
In a capital case, “while the movant need not always show a probability of success on the merits, he must present a substantial case on the merits when a serious legal question is involved and show that the balance of the equities [i.e. the other three factors] weighs heavily in the favor of granting the stay.” O’Bryan v. McKaskle, 729 F.2d at 993 (quoting Ruiz v. Estelle, 666 F.2d at 856).
Celestine, 823 F.2d at 77. As Byrne has failed to present a substantial case on the merits and has failed to demonstrate that the balance of the equities weighs heavily in his favor, there is no ground for the issuance of a stay and, therefore, the stay previously granted by the district court is vacated.
[519]*519VI.
For the foregoing reasons, we DENY Byrne’s application for a certificate of probable cause to appeal. In addition, we GRANT the state’s petition to vacate the stay of execution granted by the district court.