Appealability is the first and last issue that we resolve in this case. On May 9 of last year, the district judge dismissed the plaintiffs suit for failure to prosecute it, but the judgment order — the separate document required by Rule 58 of the Federal Rules of Civil Procedure — of dismissal was not docketed until June 10. Meanwhile, on June 1, the plaintiff had filed a motion to vacate the dismissal, and the judge had denied that motion on June 8 and the denial was docketed on June 10. On June 9 the plaintiff had filed a motion to reconsider the June 8 denial and the judge denied that motion on June 16 and the denial was docketed that day. On June 22 the plaintiff filed a second motion to reconsider the denial of his first motion, the motion to vacate the dismissal of his suit. The judge denied this motion on July 14 and the denial was docketed the following day. None of the three motions indicated what federal rule of procedure authorized it. On August 10 the plaintiff (represented throughout by counsel, be it. noted) filed a notice of appeal from the orders denying all three of his filings — the motion to vacate the dismissal of the case and the two motions to reconsider the denial of that initial motion.

A motion to alter or amend a judgment is deemed filed under Rule 59(e) of the civil rules, which tolls the time for filing an appeal from the judgment, if the motion is filed within 10 days after entry of the judgment, which means after the Rule 58 judgment order has been docketed. Fed.R.Civ.P. 58(b)(2); Laborers’ Pension Fund v. A & C Environmental, Inc., 301 F.3d 768, 775 n. 5 (7th Cir.2002); Connecticut ex rel. Blumenthal v. Crotty, 346 F.3d 84, 92 (2d Cir.2003). It is deemed filed under Rule 59(e) even if, as in this case, the motion is not labeled a Rule 59(e) motion and, again as in this case, does not say “alter or amend” (the language of Rule 59(e)), but instead uses a synonym, such as “vacate” or “reconsider.” Curry v. United States, 307 F.3d 664, 666 (7th Cir.2002); Charles v. Daley, 799 F.2d 343, 347 (7th Cir.1986); Jones v. UNUM Life Ins. Co. of America, 223 F.3d 130, 136-37 (2d Cir.2000); Harcon Barge Co. v. D & G Boat Rentals, Inc., 784 F.2d 665, 668 (5th Cir.1986) (en banc).

But we and most other courts do not cavil if, as also in this case, the motion is filed before the Rule 58 judgment order has been docketed or even before there is a Rule 58 judgment, provided that a final judgment has been rendered. E.g., Dunn v. Truck World, Inc., 929 F.2d 311 (7th Cir.1991); Havird Oil Co. v. Marathon Oil Co., 149 F.3d 283, 288 (4th Cir.1998); Kersey v. Dennison Mfg. Co., 3 F.3d 482, 485 n. 7 (1st Cir.1993); cf. Fed. R.App. P. 4(a)(2); FirsTier Mortgage Co. v. Investors Mortgage Ins. Co., 498 U.S. 269, 111 S.Ct. 648, 112 L.Ed.2d 743 (1991); Chicago United Industries, Ltd. v. City of Chicago, 445 F.3d 940, 943 (7th Cir.2006). Rule 58 prescribes a formality, a useful one but not one that is prerequisite to appealing. The[*700] losing party can appeal a judgment (in this case, the dismissal of the suit on May 9) before the entry of the Rule 58 judgment order if though not embodied in the separate document that Rule 58 requires the judgment really is final within the meaning of 28 U.S.C. § 1291. Bankers Trust Co. v. Mallis, 435 U.S. 381, 98 S.Ct. 1117, 55 L.Ed.2d 357 (1978) (per curiam); Otis v. City of Chicago, 29 F.3d 1159, 1165 (7th Cir.1994); Lazy Oil Co. v. Witco Corp., 166 F.3d 581, 585-87 (3d Cir.1999). And that just means: if the district judge is finished with the case. Chase Manhattan Mortgage Corp. v. Moore, 446 F.3d 725, 726 (7th Cir.2006); see Moreau v. Harris County, 158 F.3d 241, 244 (5th Cir.1998). By the same token, the party should be allowed to file a motion to alter or amend the judgment within the time permitted for such motions even if the Rule 58 judgment order has not yet been made or docketed.

But the first such motion that the plaintiff filed was denied on June 8 and docketed on June 10, which was when his 30-day period for appealing began to run. Fed.R.Civ.P. 58(a)(1)(D), (b)(1). He did not file his notice of appeal until August 10, which was too late. His second motion was also denied more than a month (June 16) before he filed his notice of appeal. However, his third motion, filed on June 22, was filed within 10 business days after the Rule 58 judgment order (and so it was a Rule 59(e) motion) and was denied fewer than 30 days before he filed his notice of appeal. The question concerning the appealability of the order denying that motion is not whether the appeal was untimely, which it was not, but whether the denial was an appealable kind of order.

Abbs v. Sullivan, 963 F.2d 918, 925 (7th Cir.1992), holds that the denial of a timely Rule 59(e) motion is not appealable separately from the judgment that it seeks to alter or amend. See also Cardoza v. CFTC, 768 F.2d 1542, 1546-47 (7th Cir.1985); 6A Moore’s Federal Practice ¶ 59.15[1], at p. 59-288 and n. 4 (3d ed.2006); cf. Foman v. Davis, 371 U.S. 178, 181, 83 S.Ct. 227, 9 L.Ed.2d 222 (1962); contra, Fiore v. Washington County Community Mental Health Center, 960 F.2d 229, 232-33 and n. 8 (1st Cir.1992) (en banc). The two orders — the judgment and the denial of the motion to change it— merge. They merge because the purpose of the motion, so far as suspending the time within which to appeal is concerned, is to delay the appeal from the judgment until the district court has ruled on the motion, at which point the judgment is ripe for review. Since that is the only purpose of the motion should it be denied, the court of appeals will construe an appeal from the denial (should the appellant’s notice of appeal mistakenly cite only the denial) as an appeal from the judgment. Foman v. Davis, supra, 371 U.S. at 181, 83 S.Ct. 227; Tango Music, LLC v. DeadQuick Music, Inc., 348 F.3d 244, 247 (7th Cir.2003). The notice of appeal in this case mentions only the orders denying the motions to vacate or reconsider the dismissal of his suit; that dismissal was the underlying judgment.

But by August 10, when the plaintiff filed his notice of appeal, the time for appealing from that judgment had lapsed. For only the first Rule 59(e) motion tolls the time to appeal from the judgment, unless the judgment is subsequently altered, Charles v. Daley, supra, 799 F.2d at 348, which did not happen here. E.g., Berwick Grain Co. v. Illinois Dep’t of Agriculture, 189 F.3d 556, 558 (7th Cir.1999); Charles v. Daley, supra, 799 F.2d at 347; In re Stangel, 68 F.3d 857, 859 (5th Cir.1995) (per curiam); Moody v. Pepsi-Cola Metropolitan Bottling Co., 915 F.2d 201, 206 (6th Cir.1990). Otherwise a liti[*701] gant could extend the time to appeal indefinitely simply by filing successive Rule 59(e) motions. Venable v. Haislip, 721 F.2d 297, 299 (10th Cir.1983) (per curiam). If the denial of the plaintiffs June 22 motion were appealable, he would have succeeded in circumventing the rule that only the first Rule 59(e) motion tolls the time for appealing from the judgment, because by asking us to reverse the denial of the June 22 motion he would, by reason of the merger doctrine we mentioned, be attacking the underlying judgment.

Now it is true that just as the entry of the Rule 58 judgment order on June 10 started the clock running that limits the time for appealing, Fed. R.App. P. 4(a)(1), (7), so it started the clock running that limits the time for filing a Rule 59(e) motion. For that motion must be filed within 10 days of the entry of judgment, which occurs when the Rule 58 judgment order is docketed (or, so far as the time to appeal is concerned, when 150 days have elapsed since the final judgment was issued. Fed. R.App. P. 4(a)(7)(A)(ii)). Otherwise all the plaintiffs postjudgment motions (construed as Rule 59(e) motions) would have been untimely, for they were filed more than 10 days after the district court rendered judgment on May 9.

But it does not follow that because the motions filed on June 1 and June 9 were premature, having been filed before the Rule 58 judgment order was docketed, they should be ignored and the motion filed on June 22 considered the first Rule 59(e) motion rather than a repetition of the previous motions. Nothing in the rules compels such a result, and it would not make good sense. The appellate rules provide a safe harbor for litigants uncertain whether a judgment that is not entered on a separate document as required by Rule 58 really is a final, appealable judgment. The plaintiff in our case took advantage of the safe harbor by filing his first Rule 59(e) motion more than 10 days after the judgment was rendered (May 9) but fewer than 10 days after the Rule 58 judgment order was docketed (June 10). He was protected because, as we noted earlier, a premature Rule 59(e) motion is timely. There is no reason to allow him to file a second identical motion and get more time to appeal just because his first motion was premature. He should not be rewarded for prematurity.

There is a final wrinkle to smooth out. Although most cases continue to state that motions attacking a judgment that are filed within 10 days after docketing are to be deemed Rule 59(e) motions regardless of label — and we have used that usage in this opinion — Rule 4(a)(4)(A)(vi) of the Federal Rules of Appellate Procedure was added in 1993 to provide that a Rule 60(b) motion filed within 10 days also tolls the time for appealing. See Kunik v. Racine County, 106 F.3d 168, 173 (7th Cir.1997); Jennings v. Rivers, 394 F.3d 850, 855 and n. 4 (10th Cir.2005). Under the old “labels don’t matter” approach, a Rule 60(b) motion filed within 10 days would be evaluated under the standard applicable to Rule 59(e) motions. Under the amended appellate rule, a motion labeled a Rule 60(b) motion filed within 10 days after the judgment tolls the time for appeal, just like a Rule 59(e) motion, though now, as explained in the Jennings case, the motion is evaluated by the district court under the standard set forth in Rule 60(b). But a litigant should no more be able to extend the time for appealing from the final judgment indefinitely by filing successive Rule 60(b) motions, or for that matter by filing an alternating sequence of Rule 59(e) and Rule 60(b) motions, than to do so by filing just a succession of Rule 59(e) motions. So it would not help the plaintiff for us to recharacterize any of his motions as Rule[*702] 60(b) motions, unless the motions stated a basis for relief under Rule 60(b), such as fraud on the court. They do not.

Since none of the three orders that the plaintiff is asking us to review is within our jurisdiction, the appeal is

Dismissed.