opinion: PER CURIAM.
  This motion to dismiss the defendant’s appeal raises the recurrent — one might almost say incessant — problem of distinguishing between motions under Rules 59(e) and 60(b) of the Federal Rules of Civil Procedure. See A.D. Weiss Lithograph Co. v. Illinois Adhesive Products Co., 705 F.2d 249 (7th Cir.1983) (per curiam).
  The district court entered a final judgment on April 4, 1983, awarding the plaintiff damages on its claim and the defendant a smaller sum as damages on its counterclaim. The defendant filed a notice of appeal to this court on April 8. On April 13 the plaintiff moved the district court, pursuant to Rule 59(e), for an order amending its judgment to provide that the award to the defendant on the counterclaim “be set off and satisfied by a portion of the recovery of” the plaintiff on its claim. The plaintiff asks us to dismiss the defendant’s appeal on the ground that the filing of the Rule 59(e) motion divested us of jurisdiction of the appeal. The defendant concedes the general principle, on which see, e.g., Inryco, Inc. v. Metropolitan Engineering Co., 708 F.2d 1225, 1232 (7th Cir.1983), but argues that the plaintiff’s Rule 59(e) motion is really a Rule 60(b) motion, and therefore that the motion to dismiss the appeal should be denied, since the filing of a Rule 60(b) motion does not affect the appeal.
  Post-judgment motions filed within 10 days should where possible be construed as Rule 59(e) motions to avoid otherwise endless hassles over proper characterization. The possibilities of abusive use of post-judgment motions to delay appeal are slight since 10 days is a short time and cannot be extended, see Rule 6(b). Of course there are some limitations on construing a post-judgment motion as a Rule 59(e) motion; in particular, a motion for an extension of time in which to file a motion to alter or amend the judgment may not be construed as a Rule 59(e) motion, see A.D. Weiss, supra, 705 F.2d at 250, lest Rule 6(b) be circumvented; but that is not a problem here.
  The plaintiff wanted the district judge to provide in the judgment for a set-off. This was a request to alter the judgment and was therefore a proper request to make in a Rule 59(e) motion. The only peculiarity of this case is that the Rule 59(e) motion was filed after the defendant had filed its notice of appeal. The defendant argues vigorously that the motion was filed purely to delay the appeal. However, if a party that wants to appeal a district court judgment files his notice of appeal within 10 days of entry of judgment, as the defendant did here, he runs the risk that our jurisdiction over his appeal will be divested by the other party’s filing a Rule 59(e) motion, as he is entitled to do, within the same 10-day period. The immediate filing of a notice of appeal cannot be allowed to defeat the appellee’s rights under Rule 59(e). It is unusual for the appellee— the winner below — to be filing a Rule 59(e) motion, but by no means unheard of. A prevailing plaintiff may, for example, want the judge to increase the amount of the judgment, as happened in Western Transport Co. v. E.I. Du Pont de Nemours & Co., 682 F.2d 1233 (7th Cir.1982). Or both parties may as in this case be winners and losers in the district court. We therefore caution parties that do not want .to run the risk of having their appeals dismissed as premature to wait 10 days before filing the notice of appeal.
  The appeal is
  Dismissed.