POSNER, Chief Judge.

The district court denied Boyko's petition for habeas corpus as untimely. Boyko appealed, and while the appeal was pending filed a motion under Fed.R.Civ.P. 60(b) to vacate the district court's order denying his petition. The district judge responded on April 7 by purporting to grant the motion and by setting the matter for a hearing on May 3. Boyko asked us to remand the case to the district court while retaining jurisdiction over the appeal. We refused, indicating that an opinion explaining our grounds would follow. On May 3, after the hearing, the district judge purported to grant the Rule 60(b) motion, ruling that the petition for habeas corpus had been timely after all.

The procedure the judge followed was irregular in three, possibly four, respects. First, the order of April 7, while purporting to grant the Rule 60(b) motion, was, as we know from the court's later order and also from its setting the matter for a hearing, in fact merely an order directing a hearing. The form of the order, however — its purporting to grant the Rule 60(b) motion — may have fooled Boyko into thinking that he should ask us to remand the case in order to empower the district judge to grant him the relief sought. Yet the judge hadn't actually indicated a disposition to grant the Rule 60(b) motion, only to consider doing so. If we remanded the case without retaining jurisdiction and the judge after the hearing denied the Rule 60(b) motion, Boyko would (subject to a possible qualification about to be noted) have exchanged an appeal from the denial of habeas corpus for the much more restricted appellate review of an order denying Rule 60(b) relief, Cincinnati Ins. Co. v. Flanders Electric Motor Service, Inc., 131 F.3d 625, 628 (7th Cir. 1997); Provident Savings Bank v. Popovich, 71 F.3d 696, 698 (7th Cir. 1995), since the time for appealing the denial of habeas corpus would have expired.

This is assuming that the proper course, when the court of appeals remands a case because the district judge has indicated an intention to grant the appellant's Rule 60(b) motion, is to remand the entire case, rather than to order merely a limited remand so that the appeal from the original judgment remains pending while the district court acts on the motion. But the assumption is proper (our 7th Cir.R. 57 so states, though Fobian v. Storage Technology Corp., 164 F.3d 887 (4th Cir. 1999), is contra), because the grant of the Rule 60(b) motion operates to vacate the original judgment, leaving nothing for the appellate court to do with it — in fact mooting the appeal. Limited remands are appropriate primarily to perfect appellate jurisdiction (for example, by entering judgment under Fed.R.Civ.P. 54(b)), thus enabling the appeal to go forward. Caterpillar, Inc. v. NLRB, 138 F.3d 1105, 1107-08 (7th Cir. 1998) (chambers opinion); cf. 16 Charles Alan Wright, Arthur R. Miller Edward H. Cooper, Federal Practice and Procedure § 3937.1 (2d ed. 1996).

We acknowledge that in a case such as this the unlimited remand is not a completely satisfactory solution. Suppose that the district court, on remand, thinks better of his inclination to grant the Rule 60(b) motion, and denies it; is the plaintiff remitted to the limited appellate review conventionally accorded rulings on such motions? And what about the defendant in a case in which the Rule 60(b) motion is granted before he has had a chance to argue to the appellate court that the original judgment was correct — is he, too, remitted to the limited appellate review of such grants? Probably the answer to both questions is "no," the scope of review of Rule 60(b) orders is flexible and can be expanded where necessary to give each party a full review of the district court's original judgment. But what is clear, and is all that is important here, is that it is premature to relinquish appellate jurisdiction before the district court has given any indication of its likely response to the Rule 60(b) motion.

A second and deeper problem with the district judge's order of April 7 is that it was void, at least insofar as it purported to grant Boyko's Rule 60(b) motion (the significance of this qualification will become clear shortly). The filing of the appeal had deprived the district court of jurisdiction over the case. With exceptions not applicable here but listed in Kusay v. United States, 62 F.3d 192, 194 (7th Cir. 1995), and Venen v. Sweet, 758 F.2d 117, 120 n. 2 (3d Cir. 1985), the district court and the court of appeals do not share jurisdiction over the same case. Griggs v. Provident Consumer Discount Co., 459 U.S. 56, 58, 103 S.Ct. 400, 74 L.Ed.2d 225 (1982) (per curiam); United States v. Ienco, 126 F.3d 1016, 1018 (7th Cir. 1997); Kusay v. United States, supra, 62 F.3d at 193. Jurisdiction is either all in one court or all in the other. This rule is necessary to prevent one court's stepping on the toes of the other, which would waste judicial time as well as forcing the parties to proceed in two courts in the same case at the same time. So Judge Sharp had no power to grant Boyko's Rule 60(b) motion.

Nor, though this is a closer question, on which we can find no reported case, did the judge have the lesser power to order a hearing on the motion (though this depends, as we're about to see, on just what he meant by "hearing"). The consequence of such an order would be proceedings in the case at the same time in both courts. Such a result would be in conflict not only with the rule against overlapping jurisdiction but also with the district court's specific implementing duty to review any Rule 60(b) motions filed during the pendency of an appeal "expeditiously, within a few days of their filing, and quickly deny those which appear to be without merit, bearing in mind that any delay in ruling could delay the pending appeal." Commonwealth of Puerto Rico v. SS Zoe Colocotroni, 601 F.2d 39, 42 (1st Cir. 1979) (footnote omitted); see also Brown v. United States, 976 F.2d 1104, 1110-11 (7th Cir. 1992); Graefenhain v. Pabst Brewing Co., 870 F.2d 1198, 1211 (7th Cir. 1989); Fobian v. Storage Technology Corp., supra, 164 F.3d at 890.

Our conclusion that the district judge lacked jurisdiction to order a hearing depends, however, on what exactly he meant by a "hearing," which is not clear from the record. If he meant an evidentiary hearing, then as just explained he exceeded his authority, because that would imply just the sort of duplication of effort that the rule against shared jurisdiction is designed to head off. But if all he meant was that he wanted to hear an oral argument on the Rule 60(b) motion rather than decide the motion on the papers, this would not offend the rule. The power to consider a motion implies the power to employ appropriate procedures for clarifying the issues raised by it, provided the procedures do not involve an evidentiary hearing or other time-consuming procedure that would have the potential to whipsaw the parties between the trial and appellate courts.

This assumes that the district court is at least authorized to deny a Rule 60(b) motion pending appeal; if not, if he has no power to consider such a motion while an appeal is pending, then he would lack the power to order proceedings, such as oral argument, ancillary to such consideration. But we are among the courts that hold that the judge does have the power to deny, though not to grant, a Rule 60(b) motion filed while an appeal is pending. E.g., Kusay v. United States, supra, 62 F.3d at 195; Cashner v. Freedom Stores, Inc., 98 F.3d 572, 579 n. 4 (10th Cir. 1996); United States v. Contents of Accounts, 971 F.2d 974, 988 (3d Cir. 1992); Hoai v. Vo, 935 F.2d 308, 312 (D.C. Cir. 1991); Toscano v. Chandris, S.A., 934 F.2d 383, 386-87 (1st Cir. 1991); cf. United States v. Cronic, 466 U.S. 648, 667 n. 42, 104 S.Ct. 2039, 80 L.Ed.2d 242 (1984). Unlike an order either granting the motion or setting it for a hearing, a denial of the motion does not alter the judgment that is under appeal and therefore does not (unless it spawns substantial ancillary proceedings, such as an evidentiary hearing) interfere with or threaten to duplicate the appellate proceedings.

Other courts, however, do not permit the district judge even to deny a Rule 60(b) motion if the case is on appeal. E.g., SEC v. Johnston, 143 F.3d 260, 263 (6th Cir. 1998); Long v. Bureau of Economic Analysis, 646 F.2d 1310, 1318 (9th Cir.), vacated on other grounds, 454 U.S. 934, 102 S.Ct. 468, 70 L.Ed.2d 242 (1981). One court is, apparently unwittingly, on both sides of the issue. Compare, e.g., Selletti v. Carey, 173 F.3d 104, 109 (2d Cir. 1999), and Toliver v. County of Sullivan, 957 F.2d 47, 49 (2d Cir. 1992) (per curiam), with, e.g., New York State National Organization for Women v. Terry, 886 F.2d 1339, 1349-50 (2d Cir. 1989), and Contemporary Mission, Inc. v. U.S. Postal Service, 648 F.2d 97, 107 (2d Cir. 1981). Quite apart from the division of authority, the issue cannot be considered free of doubt. There is something unquestionably anomalous about allowing the district court to issue a nonministerial order in a case over which it has lost jurisdiction. But this is not the case in which to revisit the issue. Judge Sharp did not deny the Rule 60(b) motion; he (eventually) granted it. No court permits the district court to grant a Rule 60(b) motion while the case is on appeal — which means that Judge Sharp's order of May 3, the order that really and truly granted the motion, was also beyond the judge's power — indeed more clearly than his original order, directing a hearing — because the appeal was still pending then.

The procedure that the judge (and Boyko) should have followed, under the precedents in this circuit, is this: if the judge thought there was some chance that he would grant the Rule 60(b) motion, but he needed to conduct an evidentiary hearing in order to be able to make a definitive ruling on the question, he should have indicated that this was how he wanted to proceed. Boyko would then have asked us to order a limited remand to enable the judge to conduct the hearing. If after the hearing the judge decided (as we know he would have, since he did) that he did want to grant the Rule 60(b) motion, he should have so indicated on the record and Boyko would then have asked us to remand the case to enable the judge to act on the motion and we would have done so. 7th Cir.R. 57; Adams v. City of Chicago, 135 F.3d 1150, 1153 (7th Cir. 1998); 11 Charles Alan Wright, Arthur R. Miller Mary Kay Kane, Federal Practice and Procedure § 2873 (2d ed. 1995). As we explained earlier, this would not be a limited remand but the scope of our eventual review of any appeal taken from the order entered by the district court on remand would depend on the nature of that order.

To expedite matters, we shall construe the judge's void order of May 3 as a statement of the judge's intention to grant Rule 60(b) relief and thus to reinstate the petition for habeas corpus. On that premise we remand the case to the district court to enable Judge Sharp to enter the appropriate Rule 60(b) order.