63 F.3d 160
2d Cir.
1995
OAKES, Senior Circuit Judge:

This appeal is by the North River Insurance Company (“North River”) from a final order of the United States District Court for the Southern District of New York, Charles S. Haight, Jr., Judge, denying a motion to confirm and granting a cross-motion to vacate an arbitration award on the grounds that an earlier order of the court consolidating two separate arbitrations into one was beyond the scope of the court’s powers after our decision in Government of United Kingdom of Great Britain v. Boeing Co., 998 F.2d 68 (2d Cir.1993), thus invalidating the arbitration. Because Boeing did not, in a real sense, change the law of this circuit and because the reinsurers chose not to appeal the district court’s original order consolidating the arbitrations, and because a balance of the equities requires that the award stand, the district court abused its discretion in reopening its prior order and vacating the arbitration award. Judgment reversed and case remanded.

BACKGROUND

North River insured GAF Corporation (“GAF”) under a liability policy in effect for three annual policy periods commencing May 1, 1970. GAF was subsequently involved in many lawsuits in which it paid damages arising out of exposure to its asbestos products. North River’s рolicy obligated it to cover such claims in the amount of $5 million in each of the three policy periods. Consequently, it paid out a total of $15 million to GAF.

*162Appellees are domestic and foreign rein-surers. The domestic reinsurers are Philadelphia Reinsurance Corporation, Reinsurance Corporation of New York, and Assieura-zioni Generali and Exсess and Casualty Reinsurance Association (the “U.S. reinsurers”). The foreign reinsurers are Underwriters and Underwriting Syndicates at Lloyd’s of London, and foreign companies subscribing to reinsurance contract no. R64939 (the “London reinsurers”). The U.S. and London rein-surers, along with seven other reinsurers, reinsured North River under so-called “treaty programs” in effect during the three annual policy periods at issue.

A reinsurance treaty is an ongoing contractual relationship between two insurance companies in which the primary insurer agrees in advance to cede, and the reinsurer to accept, specified business that is the subject of the contract. Under a treaty, a rein-surer agrees to indemnify a primary insurer with respect to a portiоn of the primary insurer’s liability in a designated line of business. In this ease, which is, apparently, typical, the reinsurance treaty involved the participation of many reinsurers, each accepting a percentage of the total liability under a single treaty.

The London reinsurers participated only in so-called “second layer treaties” involving a layer of $4 million of coverage in excess of a $1 million per occurrence. They agreed to an aggregate endorsement which gave North River certain options to combine products liability claims and submit them to the London reinsurers for coverage under various formulae. The aggregate endorsement was not included in the treaties to which the U.S. reinsurers subscribed.

North River, having paid GAF under its primary policies, presented claims to the reinsurers. While the seven other reinsurers paid North River, the U.S. and London rein-surers declined to pay claims, in whole or in part, contending that the asbestos claims arose from “multiple occurrences,” while North River contended that only one occurrence was involved. Calculаtions in respect of the London reinsurers were further complicated by the effect of the aggregate endorsement.

In December 1988, North River commenced arbitration proceedings against the U.S. reinsurers, and on October 3, 1989, served a separate notice of intention to arbitrate against the London reinsurers.1 The London reinsurers and the U.S. reinsurers chоse the same arbitrator, and North River appointed the same arbitrator in both proceedings, but the two arbitrators were unable to choose a third. It was at that point, October 30, 1989, that North River commenced this independent proceeding pursuant to the Federal Arbitration Act (“FAA”), 9 U.S.C. §§ 1-16 (1994), seeking an order consolidating the two proceedings against the U.S. reinsurers аnd the London reinsurers, appointing a third arbitrator or “umpire,” and compelling the reinsurers to proceed. The U.S. reinsurers and the London reinsur-ers, while having agreed to single arbitra-tions between the members of each group, objected to consolidation of the two separate proceedings before one panel of arbitrators.

In a memоrandum opinion and order dated May 23, 1991, Judge Haight overruled the reinsurers’ objections and ordered a consolidated arbitration, relying on Compania Espanola de Petroleos, S.A v. Nereus Shipping, S.A., 527 F.2d 966 (2d Cir.1975), cert. denied, 426 U.S. 936, 96 S.Ct. 2650, 49 L.Ed.2d 387 (1976). Nereus held that under Fed.R.Civ.P., Rules 42(a) and 81(a)(3) and in light of the liberal purposes of the FAA, a district court could consolidate arbitration proceedings over the objection of the parties involved. Id. at 975. Judge Haight did not enter a judgment implementing this opinion, nor was he asked to do so by the parties, and while the U.S. reinsurers and the London reinsurers had opposed consolidation when the district court ordered it, they did not appeal the order. In a subsequently issued opinion and order dated July 19, 1991, the court appointed a third arbitrator and stated that the “Court will retain jurisdiction in the event of any post-awаrd proceedings.” The court again entered no judgment.

The arbitration proceeded on the consolidated basis as ordered by Judge Haight. *163Following discovery, hearings were held for four days in July 1993, and on October 21, 1993, the arbitration panel rendered a two-to-one award in North River’s favor. On November 5, 1993, North River petitioned ‍​​​‌‌​‌​​‌‌‌‌​‌‌​‌‌‌​‌​‌​​‌‌​​‌​‌‌​​‌‌‌‌​‌‌‌​​​‌‍the district court to confirm the award under sеction 9 of the FAA, and on November 6, 1993, the U.S. and London reinsurers cross-moved under section 10 of the same act to vacate the award on the strength of Boeing, 998 F.2d 68, which was issued on June 29, 1993. Boeing held that in a case in which the parties had agreed to arbitration in separate arbitration agreements, a district court may not order the arbitrations consolidated, absent the consent of the parties. Id. at 71-74.

The district court vacated the award and denied North River’s motion to confirm it. North River Ins. Co. v. Philadelphia Reinsurance Corp., 856 F.Supp. 850 (S.D.N.Y.1994). The court noted that it was “not at all clear that this Court’s May 23, 1991 opinion and order directing consolidation was appeal-able.” Id. at 854. In any event, the court found, it had retained jurisdiction over the case to adjudicate any post-award applications, and had “not yеt entered a final judgment.” Id. at 855. “The Second Circuit has made it plain,” the court stated, “that the law of the case doctrine may have no legitimate office to perform where a fundamental change in the governing law impacts directly upon the parties’ rights and obligations.” Id. The court held that “it is crystal clear that the Second Circuit’s opinion in Boeing overrules that aspect of Nereus upon which [it] reliеd in directing a consolidated arbitration over the objections of the two groups of Reinsurers.” Id. at 853. Consequently, the court vacated the order compelling a consolidated arbitration and the resulting arbitration award, and ordered two new, separate arbitrations. Id. at 855.

The court, lastly, held that the vacatur of the arbitration award was appropriаte “whether or not the case falls precisely within one of the grounds for vacatur specified in § 10 of the FAA.” Id. But, the court held, “if such a ground is necessary to the result ... the arbitrators in the consolidated arbitration exceeded the powers conferred upon them by the parties’ [ ] contracts, in violation of § 10(d).” Id. The court noted that “[t]o be sure, the arbitrators acted in fulfillment of this Court’s order,” but, the court continued, “Boeing makes it clear that ... I exceeded my powers; and since the arbitrators derived their powers from my order, so did they.” Id.

North River appealed.

DISCUSSION

On appeal, North River contends that the district court’s order compelling arbitration on a consolidated basis was a final, appealable order, giving it res judicata effect and making the law of the cаse doctrine inapplicable. Thus, North River argues, the district court erred in vacating the order and the resulting arbitration award.

Section 16 of the FAA, the section governing the appeal of orders concerning arbitration, distinguishes between orders issued in “independent” and in “embedded” proceedings. The section provides that if the suit is “independent,” i.e., the plaintiff seeks an order compelling or prohibiting arbitration or a declaration of whether a dispute is arbitrable, ‍​​​‌‌​‌​​‌‌‌‌​‌‌​‌‌‌​‌​‌​​‌‌​​‌​‌‌​​‌‌‌‌​‌‌‌​​​‌‍and no party seeks other relief, a final judgment ending the action is immediately ap-pealable. 9 U.S.C. § 16(a)(3); Filanto, S.P.A. v. Chilewich Int’l Corp., 984 F.2d 58, 60 (2d Cir.1993). We have interpreted this section to mean that “[i]f arbitration has been ordered, the objecting party need not await the outcome of thе arbitration before challenging the order to arbitrate.” Id.

However, if the suit is “embedded,” ie., a party has sought some relief other than an order requiring or prohibiting arbitration, orders prohibiting arbitration are immediately appealable, 9 U.S.C. § 16(a)(l)(A)-(C); Fi-lanto, 984 F.2d at 60, but orders directing arbitration are not immediately appealable, 9 U.S.C. § 16(b); Filanto, 984 F.2d at 60-61.

The case before us fits squarely within the definition of an “independent” proceeding. North River initiated this action under Sections 4 and 5 of the FAA, asking the district court to compel arbitration in its disputes with the U.S. and London reinsurers. No other relief was sought, either by North Riv*164er or the reinsurers. Cf. Filanto, 984 F.2d at 61 (order compelling arbitration in a case claiming a breach of contract is an “embedded” proceeding). Thus, the district court’s order compelling arbitration on a consolidated basis was a final order and was immediately appealable. Id. at 60.

This is so even though the district court refrained from entering a judgment on the July 1991 order and retained jurisdiction to deal with any post-award proceedings. North River, 856 F.Supp. at 855. Even where a district court retains jurisdiction to enforce an arbitration award, an order compelling arbitration in an independent procеeding is final and appealable. University Life Ins. Co. v. Unimarc Ltd., 699 F.2d 846, 849-50 (7th Cir.1983); cf. General Reinsurance Corp. v. CIBA-Geigy Corp., 853 F.2d 78, 80 (2d Cir.1988). With respect to the timing of a party’s appeal, the entry of judgment is a ministerial act. See Fed.R.App. P.Rule 4(a)(2) (“A notice of appeal filed after the court announces a decision or order but before the entry of the judgment or order is treated as filed on the date of and after the entry.”); FirsTier Mortgage Co. v. Investors Mortgage Ins. Co., 498 U.S. 269, 111 S.Ct. 648, 112 L.Ed.2d 743 (1991) (notice of appеal not fatally premature even though almost a month before entry of judgment).

As persuasively explained by Judge Pos-ner:

Th[is] situation actually is little different from what it would be if the district judge had not retained jurisdiction. If he had ordered arbitration, and left it at that, it would still be open to the parties ... to go back to him for interpretation or modification of an order ... and ... if any of them prevailed before the arbitrators on any of their claims, to bring a fresh proceeding in the court below, under 9 U.S.C. § 9, to enforce the award. Yet if the district court had not formally retained jurisdiction, neither possibility would have made the order to arbitrate nonappealable. It should make no difference that, instead, the court, presumably to save the parties the bother of having to file separate actions if they want to modify or enforce the order compelling arbitration, formally retained jurisdiction.... The difference in procedures is minor, technical, and unrelated to the purpose of the final-judgment rule; it should not affect appealability.

University Life Ins., 699 F.2d at 850.

We find no merit in the contention of the U.S. and London reinsurers that they should not be penalized fоr their failure to appeal the district court’s order because, at the time the order was issued, this circuit had not interpreted the 1988 amendments to the FAA which added Section 16 on appeals. As we noted in Filanto, 984 F.2d at 60, the distinction between “independent” and “embedded” proceedings in the 1988 amendments was not new law; it was, instead, a codification of an existing, court-created rule. See, e.g., Manning v. Energy Conversion Devices, Inc., 833 F.2d 1096, 1101-02 (2d Cir.1987) (citing, inter alia, Chatham Shipping Co. v. Fertex S.S. Corp., 352 F.2d 291, 294 (2d Cir.1965)). Likewise, it has long been the law in this circuit that an order compelling arbitration in an independent action is an appealable order. Id. at 1102.

While we find that the district court’s order compelling arbitration on a consolidated basis was final for the purpose of appeal, we need not decide whether the order has res judicata effect. Even if the рroceeding in the district court was, in some respect, open ‍​​​‌‌​‌​​‌‌‌‌​‌‌​‌‌‌​‌​‌​​‌‌​​‌​‌‌​​‌‌‌‌​‌‌‌​​​‌‍and still pending, and if we apply law of the case doctrine rather than res judicata, the district court nonetheless abused its discretion by reopening its decision to order a consolidated arbitration and by vacating the resulting arbitration award.

Under the doctrine of law of the case, “a legal decisiоn made at one stage of litigation, unchallenged in a subsequent appeal when the opportunity to do so existed, becomes the law of the case for future stages of the same litigation, and the parties are deemed to have waived the right to challenge that decision at a later time.” Williamsburg Wax Museum, Inc. v. Historic Figures, Inc., 810 F.2d 243, 250 (D.C.Cir.1987). It is generally accepted that the law of the case doctrine does not limit the power of a court, but “ ‘merely expresses the practice of courts generally to refuse to reopen what has been decided.’” *165Christianson v. Colt Industries Operating Corp., 486 U.S. 800, 817, 108 S.Ct. 2166, 2178, 100 L.Ed.2d 811 (1988) (quoting Messinger v. Anderson, 225 U.S. 436, 444, 32 S.Ct. 739, 740, 56 L.Ed. 1152 (1912) (Holmes, J.)). But while a “court sometimes may review an earlier ruling, ... [nevertheless, because there is a strong policy favoring finality the court exercises its underlying power to review earlier rulings ‘sparingly.’ ” McClain v. United States, 676 F.2d 915, 917 (2d Cir.) (citations omitted), cert. denied, 459 U.S. 879, 103 S.Ct. 174, 74 L.Ed.2d 143 (1982). A court should be “loathe” to revisit an earlier decision “in the absence of extraordinary circumstances such as where the initial decision was ‘clearly erroneous and would work a manifest injustice.’ ” Christianson, 486 U.S. at 817, 108 S.Ct. at 2178 (quoting Arizona v. California, 460 U.S. 605, 618 n. 8, 103 S.Ct. 1382, 1391 n. 8, 75 L.Ed.2d 318 (1983)).

In its opinion, the district court correctly points out that we have held that a court may depart from the law of the case “where a fundamеntal change in the governing law impacts directly upon the parties’ rights and obligations.” North River, 856 F.Supp. at 855 (citing Crane Co. v. American Standard, Inc., 603 F.2d 244 (2d Cir.1979)). We have also held, however, that the law of the case should be “disregarded only when the court has a clear conviction of error with respect to a point of law on which its previous decision was predicated.” Fogel v. Chestnutt, 668 F.2d 100, 109 (2d Cir.1981) (citations and internal quotations omitted), cert. denied, 459 U.S. 828, 103 S.Ct. 65, 74 L.Ed.2d 66 (1982). “[M]erе doubt ... is not enough to open the point for full reconsideration.” Id. (internal quotations and citation omitted).

Here, after the consolidated arbitration had already taken place, the district court reopened its decision to consolidate — a decision which the U.S. and London reinsurers did not appeal — because it found that our Boeing case had fundamentally changed the law of this circuit. North River, 856 F.Supp. at 855. However, Boeing did not truly act to change the law in this circuit. Instead, in Boeing, 998 F.2d at 72, we applied Supreme Court cases, namely Volt Info. Sciences, Inc. v. Board of Trustees, 489 U.S. 468, 109 S.Ct. 1248, 103 L.Ed.2d 488 (1989); Dean Witter Reynolds Inc. v. Byrd, 470 U.S. 213, 105 S.Ct. 1238, 84 L.Ed.2d 158 (1985); and Moses H. Cone Memorial Hosp. v. Mercury Constr. Corp., 460 U.S. 1, 103 S.Ct. 927, 74 L.Ed.2d 765 (1983), which had been handed down after Nereus but beforе the district court in this case ordered arbitration on a consolidated basis.

In a very real sense, Boeing did not overrule Nereus. First, the facts of Boeing are distinguishable in a significant way from those in Nereus: in Boeing, the parties had entered into separate contractual agreements to arbitrate, while in Nereus the parties were bound by the same arbitration agreement. Thus, it is entirely unclear whether the outcome of a case factually similar to Nereus would, after Boeing, be any different than it was in Nereus before Boeing.2 Second, while in Boeing we held that Nereus was “no longer good law” to the extеnt that it was “based on the Federal Rules of Civil Procedure and the ‘liberal purposes’ of the Federal Arbitration Act,” we also noted that “[w]e do not disturb Nereus to the extent it is based on the general equitable powers ‍​​​‌‌​‌​​‌‌‌‌​‌‌​‌‌‌​‌​‌​​‌‌​​‌​‌‌​​‌‌‌‌​‌‌‌​​​‌‍of the court and principles of contract law.” Boeing, 998 F.2d at 74. Certainly equitable principles allow for confirmation of an award in a consolidated proceeding already had, especially when the parties did not appeal from the order of consolidation. Third, Boeing was not reheard in banc, nor were any of the Second Circuit’s procedures followed for changing the law of the circuit.

Boeing does not mandate that the district court’s consolidation order be vacated in this case, after the arbitration has already gonе forward. The Boeing court explicitly left Nereus untouched to the extent that it relied on the equitable powers of the court, 998 F.2d at 74, and the equities in this case require that the award from the consolidated arbitration stand. Extensive discovery has *166already been had in the consolidated case, and the arbitration proceedings have been completed. The U.S. and London reinsurers chose nоt to challenge the consolidation on direct appeal.

In addition, the Boeing decision came down on June 29, 1993, some weeks before commencement of the arbitration hearing and almost two months before the August 1993 award against appellees. Even if learned counsel for the reinsurers did not read the slip sheet opinions of the Second Circuit or the West advаnce sheets which did not come down until September, certainly the Boeing decision was available electronically. Beyond this, it was the subject of substantial publicity and discussion in the legal community. See Deborah Pines, Consolidation of Arbitrations Invalidated2nd Circuit Panel Clarifies Question Splitting Judges, N.Y.L.J., July 8, 1993, at 1; Lawrence W. Newman & Michael Burrows, Consolidation of Arbitrations, N.Y.L.J., July 29, 1993, at 3. Though our opinion does not turn on this sequence of events, it provides support for our conclusion that the reinsurers should be bound by the award in the consolidated arbitration.

Thus, because Boeing did not, in a real sense, change the law of this circuit and because the reinsurers chose not to appeal the district court’s original order consolidating the arbitrations, and because a balance of the equities requires that the award stand, the district court abused its discretion in reopening its prior order and vacating the arbitration award.3

CONCLUSION

The district court erred in reopening its decision to order arbitration on a consolidated basis and in vacating the resulting arbitration award. The judgment is reversed and the case is remanded to the district court for the resolution of any outstanding proceedings.

Notes

. Each treaty at issue contained the same arbitration clause at Article XV thereof.

. This case, to a certain extent, falls somewhere between Nereus and Boeing. While the district court found that each reinsurer entered into separate agreements with North River, North River, 856 F.Supp. at 853-54, the arbitration clause in each agreement was identical, and the agreements were part of a single reinsurance treaty program.

. The U.S. and London reinsurers contend that the district court had the power tо vacate the arbitration award under section 10(a)(4) of the FAA, which allows a district court to vacate an award "[w]here the arbitrators exceeded their powers.” ‍​​​‌‌​‌​​‌‌‌‌​‌‌​‌‌‌​‌​‌​​‌‌​​‌​‌‌​​‌‌‌‌​‌‌‌​​​‌‍9 U.S.C. § 10(a)(4). This argument fails because section 10 does not provide an independent means of challenging the district court's order compelling a consolidated arbitration which was appealable, but which was not appealed.