Students of strategy and bargaining cut their teeth on the game of Prisoners’ Dilemma. Two prisoners, unable to confer with one another, must decide whether to take the prosecutor’s offer: confess, inculpate the other, and serve a year in jail, or keep silent and serve five years. If the prisoners could make a (binding) bargain with each other, they would keep silent and both would go free. But they can’t communicate, and each fears that the other will talk. So both confess. Studying Prisoners’ Dilemma has led to many insights about strategic interactions. See Thomas C. Schelling, The Strategy of Conflict 53-80, 119-61 (1960; 1980 rev.); Robert Axel-rod, The Evolution of Cooperation (1984). Eldon Page did not have the leisure to study the game before he had to play it.

Page and Maurice Falls were charged with armed bank robbery. On the day set for Page’s trial, the prosecutor appeared with Falls in tow. Falls had signed an agreement promising, in exchange for a lower sentence, to plead guilty and testify against Page. After the judge accepted Falls’ plea, Page caved in and pleaded guilty too. Back in jail, Falls and Page were able at last to coordinate. Each presently asked leave to withdraw his plea. Too late, the judge said. Both were sentenced and appealed. We affirmed in an unpublished order.

Page tried again, filing a petition under 28 U.S.C. § 2255 and arguing that trial counsel rendered ineffective assistance in letting him plead guilty. This was brought up short by the fact that Page had not argued on his original appeal that trial counsel was constitutionally inadequate. Because Page had fresh counsel for the appeal, the omission forfeits the point unless Page could establish “cause” for and “prejudice” from the neglect. United States v. Kovic, 830 F.2d 680, 684 (7th Cir.1987). See Wainwright v. Sykes, 433 U.S. 72, 97 S.Ct. 2497, 53 L.Ed.2d 594 (1977). Ineffective assistance of counsel is “cause”, Murray v. Carrier, 477 U.S. 478, 488, 106 S.Ct. 2639, 2645, 91 L.Ed.2d 397 (1986), so Page maintains that his appellate counsel was ineffective in failing to challenge the effectiveness of trial counsel. See Evitts v. Lucey, 469 U.S. 387, 105 S.Ct. 830, 83 L.Ed.2d 821 (1985). Page also points to other aspects of appellate counsel's performance that he finds deficient. Fearing infinite regress, the district judge brushed aside all questions concerning appellate counsel and went straight to the foundation of the claim, holding that Page’s trial counsel had supplied effective assistance and denying the petition for relief.

The first question facing us on Page’s appeal is whether ineffective assistance of counsel may be raised at all, and if so in which court. The United States Attorney insists that the attack on appellate counsel comes too late. It, too, was surrendered because not raised on appeal. Such an argument is better suited to the works of Ionesco and Beckett than to the Federal Reporter. How could appellate counsel attack his own competence? Although this is not logically impossible (counsel could say, for example, that although he knew he ought to challenge trial counsel he had not had the time to prepare a brief on the subject), it is so implausible that we cannot demand it of counsel. Few of us have insight into our shortcomings; fewer still have the nerve to flaunt our own failings. Just as trial counsel need not attack his competence during trial, appellate counsel need not protest his inadequacies. That may be left to the next step in the process without fear of forfeiture.

“Where” is slightly more difficult than “whether”. Two courts of appeals have held that the defendant’s exclusive recourse is a motion asking the court of appeals to recall its mandate on the ground of counsel’s inadequacy. Feldman v. Henman, 815 F.2d 1318, 1321-22 (9th Cir.1987); United States v. Winterhalder, 724 F.2d 109, 111 (10th Cir.1983). They reason that because district judges must obey the mandate of the court of appeals, and may not issue orders compelling appellate courts to[*302] do anything (such as hear the appeal anew, a common remedy for deficient appellate counsel), the claim must come to the court of appeals in the first instance. Other courts of appeals have allowed defendants to start in the district courts. E.g., Mack v. Smith, 659 F.2d 23, 25-26 (5th Cir.1981); United States v. DeFalco, 644 F.2d 132, 137 (3d Cir.1979). We join this latter group.

Section 2255 authorizes collateral attacks on criminal judgments. It also specifies the forum: “the court which imposed the [contested] sentence”. That statutory designation prevails even though relief may call for revision of a judgment that has been affirmed by the court of appeals. Review of existing judgments simply defines a “collateral” attack. If the court of appeals has actually considered and rejected a claim of ineffective assistance of counsel on appeal, that decision binds the district court unless there has been an intervening change of law. United States v. Mazak, 789 F.2d 580 (7th Cir.1986). But if the issue has never been presented on appeal, it is open in the district court as any other question would be under § 2255.

Relief does not require the district court to issue orders to the court of appeals. District courts may grant relief. Ineffective assistance may justify vacating and reentering the judgment of conviction, allowing a fresh appeal. It may also justify a new trial on occasion. Counsel is ineffective only if performance below the norms of the profession causes prejudice. Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 2064, 80 L.Ed.2d 674 (1984). Prejudice means a “reasonable probability that, but for counsel’s unprofessional errors, the result of the [appeal] would have been different”, id. at 694, 104 S.Ct. at 2068. Showing a “reasonable probability” but not certainty supports a new judgment and a new appeal (so that we may decide whether the outcome actually would have been different). If the showing goes further and establishes to the district court’s satisfaction that reversal would have been a sure thing, this must mean that the district judge has become convinced that there was a fatal error in the trial. That error—which may be reached once the ineffective assistance clears away the bar of Wainwright v. Sykes—requires a new trial or other remedy adequate to rectify the wrong. So whether the remedy turns out to be a new appeal or a new trial, the district judge need not issue an order binding on this court. No rule of law forbids district courts to entertain proceedings that call into question the adequacy of counsel’s performance on appeal. See Standard Oil Co. v. United States, 429 U.S. 17, 97 S.Ct. 31, 50 L.Ed.2d 21 (1976), holding that district courts do not need leave of appellate courts to entertain motions under Fed.R. Civ.P. 60(b) alleging fraud on the court. Because district courts are the best forums to conduct any inquiries into counsel’s strategic decisions that may prove necessary, we conclude that Page properly filed this petition in the district court rather than our court.

Having got this far, however, Page is stymied. For appellate counsel need not raise all possible claims of error. Jones v. Barnes, 463 U.S. 745, 103 S.Ct. 3308, 77 L.Ed.2d 987 (1983). One of the principal functions of appellate counsel is winnowing the potential claims so that the court may focus on those with the best prospects. Defendants need dedicated, skillful appellate counsel, not routineers who present every non-frivolous claim. (Recall the saw: “He needed a lawyer, and all he had was a member of the bar.”) Page has not argued that his appellate counsel failed to advocate his cause skillfully on the initial appeal. He has argued, instead, that counsel left out an issue he deems meritorious. The district court responded by deciding that trial counsel had furnished effective assistance, as if the claim of ineffective appellate counsel were equivalent to proof.

The threshold question is not whether trial counsel was inadequate but whether trial counsel was so obviously inadequate that appellate counsel had to present that question to render adequate assistance. Counsel could be constitutionally deficient in omitting a dead-bang winner even while zealously pressing other strong (but unsuccessful) claims. Page falls well short of[*303] making such a showing, however. Counsel advised Page to get the best deal he could after Falls turned against him. Page is not the first and will not be the last to feel the sting of Prisoners’ Dilemma, and the Constitution does not demand that counsel escape a predicament that game theorists consider inescapable in one-shot performances. The district judge found that Page’s lawyer prepared conscientiously for trial, made appropriate motions, and would have gone forward had Page stood on his former plea of innocence. Page insists that trial counsel lied when informing him that Falls would testify against him; as the district court observed, this is what Falls had promised to do in the written plea agreement. We need not agree with the district court’s conclusion that trial counsel was adequate to see that appellate counsel could have made a reasoned decision to pursue other arguments instead. Page’s remaining claims — that appellate counsel did not consult “meaningfully” with him in preparing the appeal, that counsel’s briefs were vague, that counsel did not file a petition for rehearing after losing — are insufficient to call into question the adequacy of the representation. See Morris v. Sloppy, 461 U.S. 1, 13-14, 103 S.Ct. 1610, 1617, 75 L.Ed.2d 610 (1983).

Affirmed.