
543 F.3d 414 (2008)
AMERITECH CORPORATION d/b/a SBC Midwest, Plaintiff-Appellant, Cross-Appellee,
v.
INTERNATIONAL BROTHERHOOD OF ELECTRICAL WORKERS, LOCAL 21, Defendant-Appellee, Cross-Appellant.
Nos. 05-2574, 05-3553, 06-4256.
United States Court of Appeals, Seventh Circuit.
Argued September 26, 2007.
Decided September 10, 2008.
Rehearing and Rehearing En Banc Denied October 8, 2008.[*]
Stephen M. Shapiro, Jeffrey W. Sarles (argued), Mayer Brown, Chicago, IL, for Plaintiff-Appellant.
*415 Gilbert A. Cornfield (argued), Cornfield & Feldman, Chicago, IL, for Defendant-Appellee.
Before MANION, EVANS, and SYKES, Circuit Judges.
SYKES, Circuit Judge.
These appeals stem from a drawn-out labor dispute between Ameritech and the International Brotherhood of Electrical Workers, Local 21, involving three arbitrations centering on what may fairly be described as the same issue. The first and third awards favored Ameritech; the second favored the Union. The question now is whether the third arbitration award trumps the second.
The third arbitration was the product of a settlement agreement resolving the parties' first two appeals in this court. Ameritech had appealed the district court's order enforcing the second arbitration award; the Union then appealed an order denying its motion to enforce that judgment and hold Ameritech in contempt. In their settlement the parties agreed to resolve this "protracted litigation" by submitting their dispute to a third arbitrator for a "final resolution" via a "special, bifurcated arbitration proceeding." This third arbitration was held, the arbitrator sided with Ameritech, and Ameritech sought to enforce the award by moving to vacate the earlier judgment pursuant to Rule 60(b) of the Federal Rules of Civil Procedure. The district court summarily denied this motion because the first two appeals were still pending here. Ameritech then appealed this order, and we consolidated all three.
We now dismiss the first two appeals based on the parties' settlement. Following the procedure described in U.S. Bancorp Mortgage Co. v. Bonner Mall Partnership, 513 U.S. 18, 29, 115 S.Ct. 386, 130 L.Ed.2d 233 (1994), and Marseilles Hydro Power LLC v. Marseilles Land & Water Co., 481 F.3d 1002, 1003-04 (7th Cir.2007), we reverse the district court's order denying Ameritech's Rule 60(b) motion and remand with instructions to vacate the earlier judgment enforcing the second award and enter judgment for Ameritech enforcing the third arbitration award. Because the parties agreed that the third arbitration would finally resolve their dispute, and the third arbitrator's award is inconsistent with the second, Ameritech is entitled to relief from the earlier judgment under Rule 60(b).

I. Background
These three consolidated appeals are the result of a lengthy and procedurally complex labor arbitration, but the crux of the dispute is a single provision in the parties' collective-bargaining agreement. Ameritech and the Union disagreed over the meaning of § 1.03 in that agreement, which provides as follows:
This Agreement covers the work customarily performed by the employees defined in Section ... 1.01, above. However, during the tenure of this Agreement, [Ameritech] may continue to contract out such work as is now customarily contracted out and has been customarily contracted out by [Ameritech] under the previous collective bargaining agreements ... represented by [the Union].... If such work to be contracted out will cause layoffs, or part-timing or prevent the rehiring of employees with seniority standing, such contracting out of work will be reviewed by [Ameritech] with the Union and allotted on the basis of what [Ameritech] is equipped to perform and what the employees represented by the Union are able and trained to perform.
*416 Section 1.03 thus governs Ameritech's ability to contract out work to nonunion workers and provides the Union with the right to review certain layoffs and the allotment of some of this work. The condition under which the Union may exercise its review-and-allotment right is the primary subject of the parties' dispute.
The genesis of this case was in late 2002, when Ameritech, facing flagging demand for its products, announced a plan to lay off some of the Union's members. Ameritech believed that it was not required to participate in the review-and-allotment process specified in § 1.03 because poor economic conditionsnot the customary contracting out covered by § 1.03had precipitated the layoffs. The Union maintained that it was entitled to a formal review and allotment under § 1.03, and when Ameritech disagreed, the parties proceeded to the first of the three arbitrations at issue here.
Arbitrator John Flagler concluded this first arbitration in December 2002, and he resolved the dispute in Ameritech's favor. Flagler agreed with Ameritech's interpretation of § 1.03, namely, that the Union must first establish that the layoffs in question were caused by customary contracting out (as opposed to some other cause) before being entitled to the review-and-allotment process. Because Ameritech established that the layoffs were caused by poor economic conditions (not contracting out), Flagler concluded that the Union was not entitled to review and allotment.
The Union filed a second grievance in the spring of 2004, arguing that it was entitled to review and allotment because Ameritech's continued use of outside contractors prevented the rehiring of the laid-off Union members. Arbitrator Richard Kasher conducted the second arbitration, and this time the result favored the Union. Kasher distinguished his postlayoff analysis from Flagler's prelayoff analysis and did not require the Union to first show that continued contracting out had caused the failure to rehire the laid-off employees. Instead, he ordered Ameritech to provide the Union with information for a formal review and allotment without that threshold showing.
The parties then moved their dispute to the District Court for the Northern District of Illinois. Ameritech filed a complaint to vacate the Kasher award, and the Union counterclaimed to enforce the award. On cross-motions for summary judgment, the district court entered judgment for the Union, upholding Kasher's decision based on the broad judicial deference that courts traditionally afford to arbitration awards. See, e.g., United Steelworkers of Am. v. Enter. Wheel & Car Corp., 363 U.S. 593, 597, 80 S.Ct. 1358, 4 L.Ed.2d 1424 (1960) (holding that any award would be enforceable so long as it "draws its essence from the collective bargaining agreement"); Ethyl Corp. v. United Steelworkers of Am., 768 F.2d 180, 183-84 (7th Cir.1985) (same). But when the court denied the Union's subsequent motions to hold Ameritech in contempt, the stage was set for two cross-appeals. Ameritech appealed the order denying its motion for summary judgment and granting judgment for the Union (Appeal No. 05-2574), and the Union appealed the denial of its motion to enforce the judgment and hold Ameritech in contempt (Appeal No. 05-3553).
The parties were then directed into appellate mediation under Rule 33 of the Federal Rules of Appellate Procedure. They emerged from that process on September 16, 2005, with an agreement to submit their dispute to a third arbitration, to be conducted in two phases. This third arbitration was conducted before Arbitrator *417 Robert Perkovich pursuant to a detailed Joint Pre-Conference Statement negotiated and signed by the parties. The statement provided that "this special, bifurcated arbitration proceeding" was "the culmination of protracted litigation between the parties through two different arbitrations, and civil actions in the U.S. District Court and 7th Circuit Court of Appeals." The statement memorialized that "the parties agreed to resolve their dispute regarding Article 1.03 through this bifurcated process" and that this third arbitration would be the "final resolution of the proper interpretation and application of Section 1.03 of the parties' Collective Bargaining Agreement relative to [the 2002 layoffs]."
Perkovich's award favored Ameritech. He held that the first award (Arbitrator Flagler's) had been incorporated into the parties' collective-bargaining agreement and was therefore controlling on the proper interpretation of § 1.03 and that Arbitrator Kasher had erred by disregarding it. Armed with Perkovich's award, Ameritech returned to the district court with a Rule 60(b) motion seeking to vacate the earlier judgment based on this third arbitration and the parties' settlement. The district court summarily denied this motion, saying only that it could not consider the motion because the two earlier appeals were still pending. Ameritech appealed this order (Appeal No. 06-4256), and we consolidated all three appeals for briefing and disposition.

II. Discussion
The parties ask us to reconcile their arbitration trilogy on the merits, but the proper resolution of these appeals beginsand endswith the settlement that brought about the third arbitration. The parties engaged in appellate settlement negotiations under Rule 33 of the Federal Rules of Appellate Procedure and explicitly agreed to submit their dispute to a third and final arbitration as a "final resolution" and "culmination" of the "protracted litigation" between themi.e., the first two arbitrations, the district court's first and second orders, and the first two appeals in this court.
Rule 33 authorizes the court of appeals to implement a settlement reached while the case is on appeal. Herrnreiter v. Chi. Hous. Auth., 281 F.3d 634, 637 (7th Cir. 2002). Unlike in the district court, however, settlement negotiations in this court are not overseen by a judicial officer; instead, they are handled by a settlement conference attorney and what occurs during negotiations is not revealed to the court. Id. We have held that the implementation of a settlement reached on appeal entails the dismissal of the appeal upon the filing of either (a) a written agreement of the parties dismissing the appeal under Rule 42(b) of the Federal Rules of Appellate Procedure, or (b) a motion to dismiss under Rule 42(b) filed by the appellant. Id.
Here we have something close to the former. At the conclusion of their settlement negotiations, the parties signed a handwritten document agreeing to be bound by the third arbitration and specifying the questions to be posed to the arbitrator in the first and second phases of this arbitration. Later, the parties signed a lengthy Joint Pre-Conference Statement describing in greater detail the parameters of the third arbitration. As we have noted, this statement outlined the "agreement between the parties to suspend litigation currently pending in the U.S. Court of Appeals for the Seventh Circuit" for the purpose of submitting the dispute to a third arbitrator for "a final resolution of the proper interpretation and application of Section 1.03 of the parties' Collective *418 Bargaining Agreement relative to [the 2002 layoffs]." These documents are properly before this court in connection with Ameritech's appeal from the district court's denial of its Rule 60(b) motion.
That the parties did not move to dismiss under Rule 42(b)the proper procedure described in Herrnreiterdoes not mean they retained the right to continue to litigate the appeal if dissatisfied with the results of the arbitration. That strikes us as absurd. An agreement to suspend appellate litigation for the purpose of submitting the dispute to arbitration as a "final resolution" cannot possibly mean that the loser of the arbitration gets to disregard the results and continue to litigate the appeal. Such an agreement would be meaningless, accomplishing nothing except for delay. We must take the third arbitration for what it was: a settlement finally resolving the first two appeals.
The Union maintains that the Perkovich award applies only to a limited number of subcontracts-not to the subcontracts primarily at issue on appeal. The third arbitration was a bifurcated proceeding in which Arbitrator Perkovich was asked first to definitively interpret § 1.03 and then in the second phase apply that interpretation to a set of "new" subcontracts (new because they were in addition to those already involved in the parties' dispute). That structure, the Union argues, means that Perkovich's interpretation of § 1.03 applies only to those subcontracts enumerated in phase two of the third arbitration.
Notably, however, this suggested limitation is not found in the parties' agreement, which nowhere states that Perkovich's interpretation of § 1.03 in phase one of the arbitration is limited to the subcontracts involved in phase two. Quite the contrary, the parties' agreement expressed their intention to bring their prolonged fight to a close-in their own words, to seek "a final resolution" of the "protracted litigation" involving the first two arbitrations. We doubt the settlement agreement was intended only to add yet another layer of complexity to § 1.03 by creating one more interpretationone applicable only to a limited number of subcontracts. Rather, the third arbitration by its terms accomplished two things: first, it resolved the parties' dispute over the interpretation of § 1.03 and contracting out (necessarily resolving the issues on appeal), and, second, it applied that resolution to the new subcontracts identified in phase two. Perkovich's decision on § 1.03 was the final one, and that decision binds the parties.
This brings us to the third appeal involving Ameritech's motion to vacate under Rule 60(b). The district court could have considered Ameritech's motion when it was presented with two facially inconsistent arbitration awardsKasher's and Perkovich'sthe latter of which was in settlement of the dispute over the former. It is true that a district court is divested of jurisdiction once a notice of appeal is filed; that has long been procedural diktat. E.g., Griggs v. Provident Consumer Disc. Co., 459 U.S. 56, 58, 103 S.Ct. 400, 74 L.Ed.2d 225 (1982); Berman v. United States, 302 U.S. 211, 214, 58 S.Ct. 164, 82 L.Ed. 204 (1937); United States v. McHugh, 528 F.3d 538, 540 (7th Cir.2008); United States v. Vitek Supply Corp., 151 F.3d 580, 584 (7th Cir.1998). This rule conserves judicial resources by preventing overlapping and potentially inconsistent decisions; whipsawing litigants between two courts is just as inconvenient for courts as it is for parties.
There are exceptions, however, and this instance is one. Boyko v. Anderson, 185 F.3d 672, 674 (7th Cir.1999) (citing Kusay v. United States, 62 F.3d 192, 194 (7th Cir.1995) (listing exceptions)). District courts possess limited authority to deny *419 Rule 60(b) motions while an appeal is still pending, allowing the court of appeals to make its resolution a final one, knowing that a district court has no desire to amend its ruling. This creates no risk of overlapping decisions, and it has been our practice to encourage district courts to respond promptly to these motions because a quick response expedites the resolution of a pending appeal. 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). Conversely, in the event a district court is inclined to grant the motion, it can make us aware of its intention and we will remand the entire case for that purpose. See 7TH CIR. R. 57; Boyko, 185 F.3d at 675; see also Brown, 976 F.2d at 1110-11; Graefenhain, 870 F.2d at 1211. We may also employ a limited remand to a district court, permitting it to conduct a hearing before ruling on the merits of the Rule 60(b) motion in this situation. Boyko, 185 F.3d at 675.
So the district judge had an option other than a summary denial of Ameritech's Rule 60(b) motion based on the still-pending appeals. In the circumstances here where the parties agreed to settle the case through a final arbitration and the ensuing arbitration award was inconsistent with the prior judgmentthe district judge had the authority under Circuit Rule 57 to advise us whether he was inclined to grant the Rule 60(b) motion.
We have previously noted that the use of Rule 60(b) in this situation is appropriate. Marseilles Hydro Power, 481 F.3d at 1003 (suggesting the applicability of Rule 60(b)(6) after a settlement on appeal). However, it is for the district court, not us, to vacate the prior judgment in light of a settlement on appeal. The general rule is that we can enforce settlement agreements reached on appeal by dismissing the appeal, but not by vacating the underlying judgment. Bonner Mall, 513 U.S. at 29, 115 S.Ct. 386; Herrnreiter, 281 F.3d at 638. That is, settlements on appeal generally result in the dismissal of an appeal. Herrnreiter, 281 F.3d at 638.
The Supreme Court explained in Bonner Mall that the parties to an appeal generally relinquish their right to challenge the judgment below when they agree to settle their dispute during their appeal. 513 U.S. at 29, 115 S.Ct. 386. Vacatur is a remedy rooted in equity, and where an appeal is dismissed as moot, vacatur traditionally requires some happenstance or fortuity that prevents a party from obtaining a review of a judgment's merits (i.e., circumstances unattributable to the parties or when mootness results from the unilateral action by the prevailing party below). Id. at 23, 115 S.Ct. 386. That has been the rule since United States v. Munsingwear, Inc., 340 U.S. 36, 40, 71 S.Ct. 104, 95 L.Ed. 36 (1950), and the Court in Bonner Mall held that mootness due to an appellate settlement was not the sort of "vagar[y] of circumstance" justifying a reviewing court's use of vacatur on the judgment of a lower court. 513 U.S. at 25, 115 S.Ct. 386.
But we do have the power to remand for the district court to vacate the inconsistent judgment under Rule 60(b). Id. at 29, 115 S.Ct. 386; Marseilles Hydro Power, 481 F.3d at 1003. Ameritech tried the Rule 60(b) route, and its appeal of the district court's denial of that motion is here, along with the first two. The parties settled the first two appeals by way of the third arbitration; the resulting award favored Ameritech and was inconsistent with the prior judgment for the Union. This is a proper ground for relief from that judgment under Rule 60(b)(6). Marseilles Hydro Power, 481 F.3d at 1003. Accordingly, in light of the appellate settlement, we DISMISS the cross-appeals (Nos. 05-2574 & 05-3553); *420 on Ameritech's appeal of the denial of its Rule 60(b) motion (No. 06-4256), we REVERSE and REMAND to the district court with instructions to vacate the judgment enforcing the second arbitration award and enter judgment enforcing the third arbitration award.
NOTES
[*]  Circuit Judges Joel M. Flaum, Ilana Diamond Rovner, and Ann Claire Williams did not participate in the consideration of this petition for rehearing en banc.
