GARWOOD, Circuit Judge:

Petitioner-appellant James D. Koch (Koch) appeals the district court's denial of his petition for writ of habeas corpus challenging his Mississippi murder conviction. We affirm.

Facts and Proceedings Below

Koch was convicted by a Mississippi state jury of murder and sentenced to life imprisonment. Upholding his conviction on direct appeal, where he was represented by his trial counsel, the Mississippi Supreme Court held, inter alia, that the evidence presented at trial was sufficient to support the jury verdict and that the trial court properly admitted rebuttal testimony as to Koch's prior violent threat against the victim. The evidence presented at trial, as well as other grounds raised on direct appeal, is set forth in detail in Koch v. State, 506 So.2d 269 (Miss. 1987). In state collateral proceedings, the Mississippi Supreme Court denied, without conducting an evidentiary hearing or rendering a written opinion, Koch's pro se application for leave to file for post-conviction relief on the following four grounds: (1) ineffective assistance of counsel; (2) counsel conflict of interest; (3) perjured testimony of three government witnesses; and (4) prosecutorial misconduct.

Koch filed a pro se petition for writ of habeas corpus with the United States District Court for the Southern District of Mississippi, alleging the same four grounds enumerated in his state collateral proceeding. See 28 U.S.C. § 2254. The court referred Koch's petition to a magistrate. Following cross-motions for summary judgment, the magistrate, without conducting an evidentiary hearing, recommended that Koch's habeas petition be denied. Because Koch had not raised any of the claims asserted in his section 2254 petition on direct state appeal, the magistrate found that Koch's perjured testimony and prosecutorial misconduct claims were procedurally barred on an adequate and independent state ground. See Miss. Code Ann. §§ 99-39-3(2), 99-39-21 (Supp. 1989) (procedural waiver of claims not raised on direct appeal absent showing of cause and actual prejudice). The magistrate also noted that the prosecutorial misconduct claim was frivolous and without merit. The magistrate was persuaded by the trial record that Koch failed to satisfy either the performance or prejudice prongs of his ineffective assistance claim and that no evidence supported his conclusory claim of conflict of interest. Koch filed written objections to the magistrate's recommendation, requesting, inter alia, an evidentiary hearing on his claims.

Because of a clerical error, Koch's habeas petition was referred to a second magistrate, who determined that summary judgment was inappropriate because of the existence of a genuine issue of material fact as to whether Koch's trial counsel provided effective assistance. Adopting the recommendation of the first magistrate, the district court denied Koch's habeas petition. The court noted that the record was sufficient to determine the validity of the claims raised by Koch so that an evidentiary hearing was unnecessary. This appeal followed.

Discussion

Koch's primary contention is that his trial counsel failed to provide constitutionally effective assistance as a matter of law. The elements of such a claim of ineffective assistance were set forth by the United States Supreme Court in Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984):

"A convicted defendant's claim that counsel's assistance was so defective as to require reversal of a conviction ... has two components. First, the defendant must show that counsel's performance was deficient.... Second, the defendant must show that the deficient performance prejudiced the defense." Id. 104 S.Ct. at 2064.

A defendant's Strickland claim fails if either of these two prongs are not satisfied. See id. at 2069.

In order to satisfy the performance prong, "the defendant must show that counsel's representation fell below an objective standard of reasonableness." Id. "The proper measure of attorney performance remains simply reasonableness under prevailing professional norms." Id. at 2065. As the Court in Strickland warned, however,

"Judicial scrutiny of counsel's performance must be highly deferential. It is all too tempting for a defendant to second-guess counsel's assistance after conviction.... A fair assessment of attorney performance requires that every effort be made to eliminate the distorting effects of hindsight.... Because of the difficulties inherent in making the evaluation, a court must indulge a strong presumption that counsel's conduct falls within the wide range of reasonable professional assistance." Id.

Even if the defendant shows that particular actions of counsel were unprofessional and unreasonable, the defendant must also

"show that there is a reasonable probability that, but for counsel's unprofessional errors, the result of the proceeding would have been different. A reasonable probability is a probability sufficient to undermine confidence in the outcome.... The assessment of prejudice should proceed on the assumption that the decisionmaker is reasonably, conscientiously, and impartially applying the standard that govern the decision." Id. at 2068.

Koch sets forth a plethora of instances of assertedly poor performance by his trial counsel. The district court, however, adopted the recommendation of the first magistrate, who concluded that Koch's counsel rendered reasonably effective assistance. The court noted that the trial record was sufficient for resolution of this issue. A determination as to the effectiveness of counsel's assistance involves a mixed question of law and fact. See Strickland, 104 S.Ct. at 2070. Thus, we review the district court's ultimate conclusion as to counsel's effectiveness de novo. See Buxton v. Lynaugh, 879 F.2d 140, 147 (5th Cir.), cert. denied, ___ U.S. ___, 110 S.Ct. 3295, 111 L.Ed.2d 803 (1990). Accord Nunnemaker v. Ylst, 896 F.2d 1200, 1202 (9th Cir. 1990).

In essence, Koch claims that his counsel did not conduct the trial based on a clear self-defense strategy. Ultimately, the jury's determination came down to a credibility choice — whether to believe Koch's testimony at trial, or that of the local sheriff and two of his investigators who testified as to certain seemingly inculpatory statements made by Koch shortly after the shooting in question. Koch asserts, for example, that his trial counsel should have made appropriate motions or objections in order to suppress these inculpatory statements. His counsel, however, did object, though without success, to the admissibility of such statements based on inadequate Miranda warnings. Moreover, Koch does not point out any other legitimate ground on which these statements could have been suppressed. This Court has made clear that counsel is not required to make futile motions or objections. See Murray v. Maggio, 736 F.2d 279, 283 (5th Cir. 1984) (per curiam).

Koch emphasizes that his counsel failed to impeach the testimony at trial of the sheriff and of one of his investigators that Koch had told them that he was standing near the bedroom door when he shot the victim, who allegedly was sitting up against the headboard of the bed at the time. The investigator had testified in a pretrial proceeding that Koch had stated that he was standing near a bedside table when he shot her. An expert witness testified at trial that the powder burns on the victim's face indicated that the muzzle of Koch's gun had been more than one inch but less than eighteen inches from her face. The law enforcement officers' testimony at trial, however, was essentially consistent with the investigator's previous testimony. At the pretrial proceeding, the investigator specifically testified that the defendant had indicated that he was approximately six feet away from the victim when he shot her. At trial, the sheriff testified that Koch had indicated that he was between six to eight feet away from her at the time. The investigator merely testified at trial that Koch had told him that, as he turned to walk out of the bedroom, the victim said she was going to kill him, and he saw a flash, turned, and fired. Also at trial, the investigator indicated on a diagram where Koch had demonstrated that he was standing at the time. The trial record indicates that the bedroom door in question was very close to the bedside table.

Koch also points out that his trial counsel failed to move for a mistrial in light of an impermissible comment as to Koch's right to remain silent by one of the investigators. On cross-examination of the investigator, Koch's counsel asked why an available tape recorder was not used to record Koch's statements after the shooting. The investigator replied that he could not explain why they had not used the recorder at that time. He noted, however, that, although he intended to do so on the following day, Koch "advised me that he no longer wanted to speak to me. And, of course, that ended it, at that point."

In general, Doyle v. Ohio, 426 U.S. 610, 96 S.Ct. 2240, 49 L.Ed.2d 91 (1976), "prohibits the use of post-arrest, post-Miranda silence to impeach a defendant's trial testimony." United States v. Morales, 854 F.2d 61, 62 (5th Cir. 1988), cert. denied, 488 U.S. 1011, 109 S.Ct. 798, 102 L.Ed.2d 789 (1989); see United States v. Cardenas Alvarado, 806 F.2d 566, 572 (5th Cir. 1986). In the present case, the investigator arguably mentioned Koch's invocation of his right to remain silent in response to cross-examination suggesting that the investigator may have fabricated his story. This line of questioning may have opened the door for the investigator's comment on Koch's silence as an attempt to bolster his own testimony. See generally 1 W. LaFave J. Israel, Criminal Procedure §§ 9.6(a), 9.6(b) (1984 Supp. 1990). Nevertheless, even if it were impermissible, such an isolated comment would constitute harmless error. See Cardenas Alvarado, 806 F.2d at 572-73, 575.

Notwithstanding the several instances of asserted ineffective assistance of counsel enumerated by Koch, we conclude that the totality of these instances do not rise to the level of clearly deficient performance as required by Strickland. In other words, because Koch has not overcome the strong presumption that his counsel's conduct fell within the wide range of reasonable professional assistance, we reject his contention that his trial counsel failed to provide constitutionally effective assistance.

Alternatively, we conclude that, even if some of the alleged errors of Koch's trial counsel were unprofessional and unreasonable, Koch has not shown that, but for these errors, there is any reasonable probability that the result of the trial would have been different. See Rushing v. Butler, 868 F.2d 800, 806 n. 6 (5th Cir. 1989). It was undisputed that Koch shot and killed the female victim while she was in bed. The evidence presented by the state showed that Koch had informed the sheriff and his investigators that he could have placed the gun in the victim's hand and that he was not sure why he shot her because he knew that she would not have shot him. Moreover, the sheriff indicated in his testimony that Koch's story was inconsistent with the apparent direction in which the bullet traveled. Finally, two rebuttal witnesses testified that, following a violent argument between Koch and the victim at a bar two to four months prior to the shooting in question, Koch held his gun close to her head and stated that, if she said one more word, he would blow her head off. See Koch, 506 So.2d at 273 (rejecting Koch's challenge on direct appeal to admissibility of this rebuttal testimony). In light of such evidence presented at trial, the asserted errors complained of by Koch, even if they amounted to ineffective assistance, are not such as to undermine our confidence in this jury verdict.

At minimum, Koch contends that the district court should have granted an evidentiary hearing with respect to his claims. This Court, however, has made clear that, "'to be entitled to a hearing on ineffectiveness, a habeas petitioner must allege facts which, if proved, would overcome the presumptions that trial counsel is effective and that trial conduct is the product of reasoned strategy decisions.'" Rushing, 868 F.2d at 806 n. 6 (quoting Taylor v. Maggio, 727 F.2d 341, 349 (5th Cir. 1984)).

Koch cites only two alleged errors by his trial counsel that potentially require the presentation of evidence beyond that in the record in order to resolve his Strickland claim. Koch emphasizes that his counsel hired a firm to do some investigative work and that their report contained statements from two local police officers who had spoken highly of Koch, an auxiliary policeman. Koch contends that his counsel should have called them as character witnesses. According to Koch, the investigative report also contained the statement of one of the sheriff's investigators that Koch had not made any conflicting statements to him on the eve of the shooting. Koch contends that his counsel should have used this prior statement to impeach the investigator at trial, who testified on cross-examination that Koch had given two versions of the shooting — in the first, after hearing the victim's threat to kill him, he reached for his weapon, turned, and fired; and, in the second, he drew his weapon, cocked the hammer, and shot her in one fluid motion. Even assuming that Koch accurately depicted the contents of the investigative report, we conclude that these two alleged errors, along with the seventeen other instances that Koch claims constitute counsel errors, satisfy neither the performance nor the prejudice prongs, as outlined in Strickland. Thus, because the record is complete and Koch's ineffective assistance claim can be resolved without the taking of additional evidence, we conclude that remand for an evidentiary hearing on this claim is unnecessary. See Ellis v. Lynaugh, 873 F.2d 830, 840 (5th Cir.), cert. denied, ___ U.S. ___, 110 S.Ct. 419, 107 L.Ed.2d 384 (1989); Rushing, 868 F.2d at 806 n. 6.

Koch raises another issue on appeal that is somewhat related to the foregoing issue as to whether his trial counsel provided effective assistance. Koch contends that the district court erred in not granting his request for an evidentiary hearing as to his claim that his counsel had an actual conflict of interest adversely affecting his representation of Koch at trial.

If this Court were to grant his request for an evidentiary hearing, Koch asserts that he "will attempt to prove that at some point" his trial counsel and the sheriff entered into an agreement whereby his counsel would not contest the sheriff's fabricated testimony as to Koch's alleged inculpatory statements. In return, according to Koch, the sheriff agreed to assure a favorable disposition of a pending narcotics prosecution for one of the other clients of Koch's counsel. Koch does not claim to have any personal knowledge of this asserted relationship or agreement between his counsel and the sheriff, nor does he allege any specific or concrete source of information (hearsay, circumstantial, or otherwise) tending to indicate that any such relationship or agreement actually existed, nor, indeed, anything specific that would even give rise to any suspicion in that respect. Koch merely "submits that the egregious manner in which [his counsel], an experienced and very competent criminal attorney, conducted this trial is sufficient proof to establish a prima facie case and require an evidentiary hearing on this claim."

In various pleadings filed with the Mississippi Supreme Court and the federal district court, Koch indicated that the sheriff had illegal gambling interests. According to Koch, the sheriff was aware that Koch likely would be the next chief of police for Bay St. Louis, Mississippi, and that he had publicly stated that, if he were the successor of the current police chief, he would fight illegal gambling in the area. In light of these bare allegations, Koch seems to deduce that the only explanation for the alleged errors of his trial counsel is collusion between his counsel and the sheriff.

The district court adopted the recommendation of the first magistrate, who concluded that Koch's conflict of interest claim should be dismissed without an evidentiary hearing. The magistrate emphasized that, aside from Koch's conclusory statements as to the sheriff's gambling interests and as to the collusion between the sheriff and his trial counsel, no factual basis tending to support this claim was alleged. The magistrate also noted that "the record amply reflects defense counsel's zealous representation of defendant."

Addressing the applicability of its ineffective assistance analysis to such conflict of interest claims, the Court in Strickland stated, "Prejudice is presumed only if the defendant demonstrates that counsel 'actively represented conflicting interests' and that 'an actual conflict of interest adversely affected his lawyer's performance.'" Strickland, 104 S.Ct. at 2067 (quoting Cuyler v. Sullivan, 446 U.S. 335, 100 S.Ct. 1708, 1719, 1718, 64 L.Ed.2d 333 (1980) (footnote omitted)); see Russell v. Lynaugh, 892 F.2d 1205, 1213-14 (5th Cir. 1989). The asserted collusive agreement or relationship between Koch's counsel and the sheriff, if it existed, would surely entitle Koch to relief. However, Koch has at best set forth conclusory allegations of such a collusive agreement or relationship. Aside from Koch's deduction from the asserted instances of errors by his counsel at trial, the totality of which we concluded above failed to establish a valid ineffective assistance claim, Koch does not suggest any basis whatever to support his allegations of counsel conflict. Although pro se habeas petitions must be construed liberally, "mere conclusory allegations on a critical issue are insufficient to raise a constitutional issue." Woods, 870 F.2d at 288 n. 3; see Ross v. Estelle, 694 F.2d 1008, 1011-12 n. 2 (5th Cir. 1983) (refusing to hold evidentiary hearing based on petitioner's bare assertions of ineffective assistance); cf. Russell, 892 F.2d at 1213-14 (concluding that petitioner failed to allege facts of actual conflict of interest warranting habeas relief and, therefore, refusing to remand for evidentiary hearing on that claim). Thus, we hold that Koch's conclusory allegations fail to establish a valid conflict of interest claim as to his trial counsel and, therefore, do not warrant remand for an evidentiary hearing.

Koch raises two additional claims of perjured testimony and of prosecutorial misconduct. These claims essentially are other ways of restating Koch's conflict of interest claim.

The district court adopted the recommendation of the first magistrate, who concluded that both of these claims were procedurally barred on an adequate and independent state ground because they could have been but were not raised on direct state appeal. See Miss. Code Ann. §§ 99-39-3(2), 99-39-21 (Supp. 1989) (procedural waiver of claims not raised on direct appeal absent showing of cause and actual prejudice).

"The Supreme Court has recently clarified the standard by which federal courts should determine 'whether a state court's ambiguous invocation of a procedural default bars federal habeas review.' Harris v. Reed, 489 U.S. 255, 109 S.Ct. 1038, 1041, 103 L.Ed.2d 308 (1989). Under Harris, a procedural default does not bar consideration of a federal claim on habeas review unless the last state court rendering a judgment on the case clearly and expressly states that its judgment rests on a state procedural bar. Id. at ___, 109 S.Ct. at 1043 (citations omitted)." Fierro v. Lynaugh, 879 F.2d 1276, 1281 (5th Cir. 1989), cert. denied, ___ U.S. ___, 110 S.Ct. 1537, 108 L.Ed.2d 776 (1990).

When Koch first raised his claims of perjured testimony and prosecutorial misconduct in state collateral proceedings, the Mississippi Supreme Court dismissed that appeal without holding an evidentiary hearing or rendering a written opinion. See note 1 and accompanying text, supra. We accordingly assume for the purposes of this decision that these claims are not procedurally barred. See Booker v. Lynaugh, 872 F.2d 100, 100-01 (5th Cir. 1989).

With respect to his perjured testimony claim, Koch asserts that the sheriff and two of his investigators lied at trial as to the inculpatory statements allegedly made by Koch shortly after the shooting — e.g., Koch was exiting the bedroom and was near the bedroom door when he shot the victim, Koch never saw a gun in the victim's hand prior to the shooting but observed only a flash out of the corner of his eye, and Koch could have placed the gun in the victim's hand after he shot her. According to Koch, this perjured testimony deprived him of his due process rights under the Fourteenth Amendment. Koch requests remand for an evidentiary hearing as to this claim.

In order for such an allegation of perjured testimony to constitute a due process violation, Koch "must show that the prosecution knowingly presented materially false evidence to the jury." United States v. Martinez-Mercado, 888 F.2d 1484, 1492 (5th Cir. 1989) (citations omitted). See generally 2 W. LaFave J. Israel, supra, § 19.5(a). Aside from his conclusory allegations of counsel conflict of interest, which we determined above did not warrant remand for an evidentiary hearing, Koch does not suggest that he has any evidence to support his perjured testimony claim. Koch simply denies, as he essentially did at trial, that he made these inculpatory statements and asserts that his "trial testimony in this case effectively contradicted the alleged false statements." Such contradictory trial testimony, however, merely establishes a credibility question for the jury. See Little v. Butler, 848 F.2d 73, 76 (5th Cir. 1988) (inconsistencies in witnesses' testimony at trial are to be resolved by trier of fact and do not suffice to establish that certain testimony was perjured). Moreover, even if we accept as true Koch's allegations of perjured testimony, Koch does not allege that the prosecution knew that this testimony was false. See id. (denying habeas petition because, even assuming, arguendo, that certain testimony was false, no proof of prosecutor's knowledge of its falsity); Hawkins v. Lynaugh, 844 F.2d 1132, 1141 (5th Cir.) (denying habeas petition because allegations demonstrate neither falsity of law enforcement officer's testimony nor State's knowing use of false testimony), cert. denied, 488 U.S. 900, 109 S.Ct. 247, 102 L.Ed.2d 236 (1988), appeal on other grounds, 862 F.2d 482, appeal after remand, 862 F.2d 487 (5th Cir. 1988) (per curiam), vacated, ___ U.S. ___, 110 S.Ct. 1313, 108 L.Ed.2d 489 (1990). Thus, we conclude that Koch's bare allegations neither establish a valid due process claim nor warrant an evidentiary hearing on such a claim.

Finally, with respect to his prosecutorial misconduct claim, Koch asserts that, where deliberately offensive prosecutorial misconduct is as egregious as that allegedly occurring at his trial, the due process and double jeopardy clauses of the Fourteenth Amendment bar retrial. Cf. Robinson v. Wade, 686 F.2d 298, 309 (5th Cir. 1982) (no intentional prosecutorial overreaching sufficient to bar retrial). See generally 3 W. LaFave J. Israel, supra, § 24.4(a). Although Koch reiterates his prior allegations as to the collusive agreement between the sheriff and his trial counsel and as to the perjured testimony of the sheriff and of the investigators, Koch fails to point to any form of prosecutorial overreaching. For example, as noted above, Koch does not even allege that the prosecution knew that the assertedly perjured testimony was false.

The district court adopted the recommendation of the first magistrate, who stated that Koch's prosecutorial misconduct claim is "utterly frivolous and without merit." We conclude that the facts as alleged by Koch do not support a valid claim of prosecutorial overreaching and, therefore, do not warrant remand for an evidentiary hearing on this claim.

For the foregoing reasons, the judgment of the district court is

AFFIRMED.