Billy Joe Edgemon appeals from the District Court’s dismissal of his petition for a writ of habeas corpus. He argues that he was denied the effective assistance of counsel, in violation of the Sixth and Fourteenth Amendments, because of numerous errors committed by his trial counsel. We believe Edgemon’s claim that his counsel had a conflict of interest was sufficiently pleaded and should not have been dismissed as conclusory. We hold that Edgemon is entitled to an evidentiary hearing on this claim. We also remand for a hearing Edgemon’s claim that counsel should have challenged one of the jurors as mentally incompetent. The other claims are without merit, and as to them we agree that the District Court’s dismissal was correct.
In 1981, Edgemon was convicted of first-degree murder and sentenced to life imprisonment. The conviction was affirmed on direct appeal. Edgemon v. State, 275 Ark. 313, 630 S.W.2d 26 (1982). He filed a petition for post-conviction relief pursuant to Rule 37, Ark.R.Crim.P., claiming that he was denied effective assistance of counsel because his trial counsel: 1) stipulated to the reading of a hearsay statement by a witness rather than deposing the witness; 2) failed to cross-examine two of the prosecution’s witnesses effectively because they were paying clients of the attorney; and 3) failed to challenge a juror who was a cousin of one of the prosecution’s witnesses. The Arkansas Supreme Court denied the petition without a hearing. Edgemon v. State, No. CR 81-110 (Ark. Dec. 5, 1983) (per curiam) (unpublished opinion). Edgemon then filed a petition for a writ of habeas corpus with the District Court claiming he was denied effective assistance of counsel for the above three reasons and also because trial counsel: 4) failed to object to inflammatory questions about Edgemon’s alcohol consumption and extramarital relations with women; 5) failed to object to a juror who was mentally incompetent; and 6) committed other irregularities too numerous to mention. The District Court dismissed the petition without holding an evidentiary hearing. It considered Edgemon’s allegations either conclusory or related to trial tactics.1
To prove a violation of the constitutional right to effective assistance of counsel defendant must show that counsel’s performance was deficient and that prejudice resulted. Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 2067, 80 L.Ed.2d 674 (1984). The defendant must *255show “that counsel's representation fell below an objective standard of reasonableness,” id. at 2065, and “that there is a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different,” id. at 2068. When reviewing counsel’s performance, a court must be highly deferential. Id. at 2065.
Dismissal of a petition without a hearing is proper if the allegations, even if true, fail to state a claim cognizable in a federal habeas corpus proceeding. Lindner v. Wyrick, 644 F.2d 724, 729 (8th Cir.), cert. denied, 454 U.S. 872, 102 S.Ct. 345, 70 L.Ed.2d 178 (1981). Dismissal is also proper if the facts are not in dispute, or if the dispute can be resolved on the basis of the record. Id. However, the district court must grant an evidentiary hearing if the defendant pleads facts which, if proved, would entitle him to relief, and he did not receive a full and fair hearing in the state court in which the merits of the factual dispute were resolved. Townsend v. Sain, 372 U.S. 293, 312-13, 83 S.Ct. 745, 756-57, 9 L.Ed.2d 770 (1963); Beavers v. Lockhart, 755 F.2d 657, 661 (8th Cir.1985).
The District Court found that trial counsel’s stipulation to a witness’s police statement rather than deposing the witness and the acceptance of the juror who was related to a prosecution witness were matters of trial tactics and did not constitute ineffective assistance. We agree. We have reviewed the record and believe that it is possible that a deposition would have been even more incriminating than the police statement. And, the juror, an acquaintance of Edgemon’s attorney, stated that he could be impartial even though his cousin would be testifying. We do not believe these tactical choices of trial counsel were deficient. Edgemon next claims his attorney should have objected to questions about his drinking habits and extra-marital affairs. Even if trial counsel erred in failing to object to these questions, the error was insignificant. In view of the evidence presented at the trial, Edgemon cannot show a reasonable probability that but for trial counsel’s alleged error the verdict would have been different. The sixth claim, that counsel made other mistakes “too numerous to mention,” is obviously too vague to deserve further inquiry.
Edgemon’s allegation that his trial attorney had a conflict of interest is of a more serious nature. In certain Sixth Amendment cases, such as denial of the assistance of counsel altogether or state interference with counsel’s assistance, prejudice is so likely that it is presumed. Strickland, 104 S.Ct. at 2067. A similar although mofe limited presumption exists when an attorney has a conflict of interest. Id. Prejudice is presumed if “the defendant demonstrates that counsel ‘actively represented conflicting interests’ and ‘that an actual conflict of interest adversely affected his lawyer’s performance.’ ” Id., citing Cuyler v. Sullivan, 446 U.S. 335, 350, 348, 100 S.Ct. 1708, 1719, 1718, 64 L.Ed.2d 333 (1980).
Edgemon alleges that his trial counsel also represented the Sheriff who helped investigate the case and one of the prosecution’s chief witnesses. There was no evidentiary hearing on this issue in the state court, and it cannot be determined from the trial record whether a conflict of interest actually existed, so the facts are in doubt. If Edgemon can prove his allegation and meet the conflict-of-interest standard set out in Strickland, he will be entitled to relief. Because this allegation concerns a breach of counsel’s loyalty, and, if true, creates a presumption of prejudice, we do not believe it should have been dismissed as conclusory. Edgemon is entitled to an opportunity to prove his allegation.
We realize that in reaching this conclusion we are placing ourselves at variance not only with the District Court, but also with the Supreme Court of Arkansas, which, we are sure, gave Edgemon’s post-conviction petition careful consideration. The major ground assigned by both these courts for rejecting the allegation of conflict of interest is that no specific example is given of any respect in which counsel’s *256cross-examination of prosecution witnesses may have fallen short. If, after an evidentiary hearing, Edgemon is unable to show what more counsel could have done, we would agree that his petition should be dismissed, but we believe such a disposition at the pleading stage is premature. He has, after all, been sentenced to life in prison. He claims that his lawyer, at the same time that he was representing Edgemon,2 also represented both one of the prosecution’s leading witnesses and the Sheriff who supervised the investigation of the crime. The lawyer may well be completely blameless, but such an allegation obviously raises a serious potential problem. No court, state or federal, has yet held an evidentiary hearing to explore it. In these circumstances, we believe Edgemon should have a chance to backup with specific evidence the allegations he makes. It cannot be said at this point, in other words, that the files and records of the case conclusively show that he is entitled to no relief, and therefore it was not appropriate to dismiss his petition without a hearing.
Edgemon also alleges that one of the jurors “suffered from a birth defect” which rendered him “[mentally in] competent to appreciate the facts, circumstances or testimony surrounding the case against” petitioner. Brief for Appellant 16-17. Counsel was ineffective, it is claimed, in not asking the trial court to strike this juror. We have cautioned that post-trial inquiries into a juror’s state of mind are not favored, and that a high standard of proof is required when an allegation of juror incompetence is made. A petitioner is entitled to a hearing only if he produces substantial evidence of incompetence “such as proof of an adjudication of insanity or mental incompetence made shortly before or after the trial.” United States v. Mauldin, 714 F.2d 854, 855 (8th Cir.1983).
Edgemon’s argument, however, is somewhat different. He is not challenging the competency of the juror directly, but rather the failure of trial counsel to make the challenge before the jury was empaneled. States are not required by the federal Constitution to try criminal cases to juries of twelve people, but whatever the number of jurors (and Arkansas adheres to the common-law tradition and requires a unanimous verdict of twelve), surely both sides are entitled to have their case heard by competent people. Again, as in the case of the charge of conflict of interest by counsel, the allegation is somewhat unspecific. We believe, however, that it deserves further exploration. On remand, Edgemon should be given a chance to show by evidence exactly what the juror’s mental condition was. (Not every mental defect or “retardation,” a term that covers many types of conditions, some far more severe than others, would be disqualifying.) Counsel’s reasoning in not raising the question of the juror’s fitness to sit should also *257be explored. He may well have an entirely satisfactory explanation.
In short, we agree with the District Court that four of Edgemon’s six claims of ineffective assistance were so clearly without merit as to deserve no further inquiry, but we vacate the judgment and remand the cause for an evidentiary hearing on the two remaining allegations, that counsel was laboring under a conflict of interest, and that counsel was constitutionally ineffective because he did not attempt to challenge a mentally defective juror.
It is so ordered.