In 1997, plaintiff-appellant Emery Air Freight lost an arbitration proceeding against Local 478, one of its New Jersey-based union locals, and pursuant to the arbitral award, assigned certain hauling routes (previously undertaken by non-union personnel) to members of Local 478. Later, Local 295, one of Emery’s New York-based union locals, claimed the same work assignments and initiated an arbitration proceeding against Emery. Emery filed suit in the United States District Court for the Eastern District of New York (Block, J.) to restrain the second arbitration proceeding and to compel the two locals to submit to three-way arbitration with Emery to resolve the dispute. The district court (i) concluded that it had the power to order three-way arbitration, but (ii) refused to exercise its discretion to do so in the circumstances of this case, and (iii) dismissed the complaint.
On appeal, Emery challenges the existence and exercise of the district court’s discretion, while Local 478 challenges subject matter jurisdiction and the court’s power to order three-way arbitration without consent of all parties.
We conclude that Section 301 of the Labor Management Relations Act confers subject matter jurisdiction over Emery’s complaint. We also hold that the district court can order three-way arbitration without mutual consent in appropriate circumstances, and that the district court possesses discretion in the exercise of this power. Finally, we conclude that the court in this case did not abuse its discretion.
BACKGROUND
Emery Air Freight ships freight domestically and internationally, by air and by truck. It frequently moves freight between John F. Kennedy International Airport (“JFK”) in New York and Newark International Airport (“Newark”) in New Jersey. Two collective bargaining agreements bear upon this case. Emery’s agreement with Local 295 covers truck drivers and dock workers in Brooklyn, Queens, the Bronx, and Long Island, in New York. Its agreement with Local 478 covers the same class of employees in Northern New Jersey. See Emery Air Freight Corp. v. International Bhd. of Teamsters, Local 295, 23 F.Supp.2d 313, 314-15 (E.D.N.Y.1998).
Each collective bargaining agreement includes an arbitration provision covering disputes between the local and Emery over the meaning or application of the agreement. Local 295 may go to the American Arbitration Association (“AAA”) if a grievance with Emery is not resolved internally in 45 days. Local 478’s agreement includes a similar but non-identical arbitration clause that requires Emery and the local to seek agreement on an arbitrator, failing which the arbitrator is to be appointed by the New Jersey Board of Mediation. Neither agreement provides for three-way arbitration. See id. at 315.
Local 478 filed a grievance with Emery in 1996 complaining that the company had violated Local 478’s collective bargaining agreement by assigning certain truck routes between JFK and locations in New Jersey to non-union workers. The dispute was settled in part, and the remaining part (involving the JFK-Newark routes) proceeded to arbitration. See id.
In September 1997, the arbitrator ruled in favor of Local 478, finding that Emery had violated the collective bargaining agreement, and deciding that the haulage between airports be assigned to members of that local. See id. Emery complied without seeking judicial review of the arbi-tral award. Local 295 did not participate in the New Jersey arbitration or seek to vacate or modify it afterwards.
On April 29, 1998, Local 295 demanded that Emery arbitrate Local 295’s claim that the JFK-Newark work rightfully belonged to its members. See id.
*88Emery promptly filed a complaint in the United States District Court for the Eastern District of New York against both locals and the American Arbitration Association (where Local 295’s demand for arbitration was pending), seeking (i) a restraining order to block the arbitration proceeding between Emery and Local 295 and (ii) an order requiring the company and the two locals to enter into three-way arbitration to resolve which local should do the disputed work. See id. at 315-16. Emery proposed that the dispute be heard by a three-member panel, one selected under the procedures in Local 295’s agreement, one selected under the procedures in Local 478’s agreement, and the third selected by the other two arbitrators (or by the district court in the absence of agreement).
At a hearing in the Eastern District, Local 295 consented to join in three-way arbitration,1 but Local 478 refused, arguing that it had a valid arbitration award and that three-way arbitration was inappropriate in this case. See id. at 316.
The district court dismissed Emery’s complaint in November 1998. The opinion concluded that the court had the authority to order three-way arbitration because Columbia Broadcasting System, Inc. v. American Recording & Broadcasting Association, 414 F.2d 1326 (2d Cir.1969), which first authorized such arbitration orders, remained good law. See Emery Air Freight, 23 F.Supp.2d at 316. But the court declined to exercise discretion to do so in this case because Local 478 had already won an arbitration award, and Emery had only itself to blame for its predicament: in light of the obvious potential for conflicting claims, the company should have negotiated three-way arbitration provisions into its agreements with the two locals, or at least should have tried to bring Local 295 into a three-way arbitration proceeding when Local 478 first filed its grievance in 1996. The court also noted that: (i) the two agreements contained incompatible provisions for selecting arbitrators; (ii) an award in the arbitration between Local 295 and Emery might not conflict with the award won by Local 478; and (iii) there are no-strike provisions in both locals’ agreements, so labor unrest was not “imminent.” Id. at 321.
DISCUSSION
The district court concluded that it had jurisdiction under Section 301 of the Labor Management Relations Act (“LMRA”), as construed by this Court in Columbia Broadcasting System, Inc. v. American Recording & Broadcasting Ass’n, 414 F.2d 1326 (2d Cir.1969) (“CBS”). See Emery Air Freight Corp. v. International Bhd. of Teamsters, Local 295, 23 F.Supp.2d 313, 316 (E.D.N.Y.1998) (citing CBS, 414 F.2d at 1328). Section 301 of the LMRA reads:
Suits for violation of contracts between an employer and a labor organization representing employees in an industry affecting commerce as defined in this chapter, or between any such labor organizations, may be brought in any district court of the United States having jurisdiction of the parties, without respect to the amount in controversy or without regard to the citizenship of the parties.
29 U.S.C. § 185(a).
The CBS opinion concluded that Section 301 provided jurisdiction over CBS’s suit to enjoin an arbitration commenced by one union and to force that union and another into three-way arbitration with CBS: “There is ample authority holding that § 301 gives the federal courts broad jurisdiction to deal with many types of controversies that arise between labor and management.” CBS, 414 F.2d at 1328.
Judge Block, relying on CBS, exercised jurisdiction to consider Emery’s complaint seeking three-way arbitration, and exer*89cised discretion to deny relief. Appellant Emery argues that the district court, having the power to order three-way arbitration, lacked discretion to deny relief, or in the alternative abused such discretion as it had. Appellee Local 478 argues that CBS is no longer good law, and that the Norris-LaGuardia Act is an independent bar to jurisdiction. We consider these arguments in reverse order.
A. Norris-LaGuardia Act
Local 478 acknowledges that CBS found jurisdiction over a claim seeking three-way arbitration, but argues that the Norris-LaGuardia Act, 29 U.S.C. §§ 101-115-not raised by the parties in CBS, and not considered in the CBS opinion — precludes jurisdiction over Emery’s complaint.
The Norris-LaGuardia Act deprives federal courts of power “to issue any restraining order or temporary or permanent injunction in a case involving or growing out of a labor dispute, except in a strict conformity with the provisions” of the Act. Id. § 101. “Labor dispute” is defined as “any controversy concerning terms or conditions of employment, or concerning the association or representation of persons in negotiating, fixing, maintaining, changing, or seeking to arrange terms or conditions of employment.” Id. § 113(c). Such a dispute may be between an employer and a union, between two employers, or between two unions. See id. § 113(a). A district court may issue an injunction regarding a “labor dispute” only if it holds a hearing, takes testimony from witnesses subject to cross-examination and makes a series of factual findings. Id. § 107.
The district court did not follow the procedure outlined in Norris-LaGuardia, and we conclude that it was not required to do so.
Local 478 casts its argument in terms of subject matter jurisdiction, noting that the Norris-LaGuardia Act uses the word “jurisdiction.” Id. § 101. The Supreme Court, however, has held that Norris-La-Guardia is a limit on remedial authority, not subject matter jurisdiction. See Avco Corp. v. Aero Lodge No. 735, Int’l Ass’n of Machinists & Aerospace Workers, 390 U.S. 557, 560-61, 88 S.Ct. 1235, 1237-38, 20 L.Ed.2d 126 (1968); see also Sheet Metal Workers Int’l Ass’n v. Seay, 693 F.2d 1000, 1003 (10th Cir.1982) (“The argument that the district courts are without jurisdiction to hear labor cases in which injunc-tive relief is sought, based on the use of the term ‘jurisdiction’ in the Norris-La-Guardia Act, was put to rest by the Supreme Court in Avco.” (footnote omitted)), modified on other grounds, 696 F.2d 780 (10th Cir.1983).
Construing Local 478’s Norris-La-Guardia argument as one about limits on the district court’s remedial authority, we reject it. Suits seeking specific performance of contractual arbitration provisions are not barred by the Norris-LaGuardia Act. See Textile Workers Union of Am. v. Lincoln Mills of Ala., 353 U.S. 448, 458-59, 77 S.Ct. 912, 919, 1 L.Ed.2d 972 (1957); see also Local 1814, Int’l Longshoremen’s Ass’n v. New York Shipping Ass’n, 965 F.2d 1224, 1236 (2d Cir.1992) (noting that federal courts may issue injunctions to effectuate federal labor law’s “strong policy favoring arbitration” (internal quotation marks omitted)). True, Emery sought an injunction blocking Local 295’s arbitration proceeding, so this case is not strictly analogous to Lincoln Mills. But Emery’s sole objective is to compel a consolidated arbitration proceeding covering the entire dispute. Moreover, Local 295 has consented to a stay of its arbitration, so that the only disputed issue in the district court was whether Local 478 should be forced to participate in a three-way arbitration. We conclude therefore that the case fell within the Lincoln Mills exception to Norris-LaGuardia.
B. The Continuing Vitality of CBS.
This Court’s first detailed opinion on three-way arbitration is CBS, in which CBS had assigned certain jobs to members *90of the union representing broadcast technicians; the union representing recording engineers commenced arbitration against CBS, claiming the same jobs; and CBS protected itself from the competing claims by initiating arbitration with the broadcast technicians’ union, and by filing an action in the district court seeking an order combining the two arbitrations into a unitary three-way proceeding. See CBS, 414 F.2d at 1327. The district court granted CBS’s motion, and the recording engineers appealed. See id.
As noted previously, the Court in CBS concluded that the LMRA conferred jurisdiction, see id. at 1327-28, and then considered whether the court had the power to order a three-way arbitration even though neither collective bargaining agreement authorized it, see id. at 1328-29. CBS rejected a strict application of “common law contract principles,” and relied on language in United Steelworkers of America v. Warrior & Gulf Navigation Co., 363 U.S. 574, 80 S.Ct. 1347, 4 L.Ed.2d 1409 (1960), which characterized a collective bargaining agreement as “ ‘more than a contract,’ ” and observed: “ ‘It calls into being a new common law — the common law of a particular industry or of a particular plant.’ ” CBS, 414 F.2d at 1328 (quoting United Steelworkers, 363 U.S. at 578-79, 80 S.Ct. at 1351). So guided, and following a Railway Labor Act case in which the Supreme Court had ordered three-way arbitration in the absence of contractual authorization, we concluded in CBS that the district court had power to order that remedy. Id. at 1328-29 (citing Transportation-Communication Employees Union v. Union Pac. R.R. Co., 385 U.S. 157, 161, 87 S.Ct. 369, 371, 17 L.Ed.2d 264 (1966)).
Finally, CBS considered whether the district court had properly exercised its power to order three-way arbitration in that case, and affirmed, noting that (i) the two collective bargaining agreements included “broad arbitration provisions”; (ii) the broadcast technicians had consented to arbitrate pursuant to the format described in the recording engineers’ collective bargaining agreement, so there would be no procedural incompatibility; and (iii) a three-way arbitration would prevent “ ‘duplication of effort [and] the possibility of conflicting awards.’ ” Id. at 1329 (quoting Columbia Broad. Sys., Inc. v. American Recording & Broad. Ass’n, 293 F.Supp. 1400, 1403 (S.D.N.Y.1968)).
Local 478 argues that CBS is no longer good law, having been overruled sub silen-tio by this Court’s intervening opinion in Government of the United Kingdom of Great Britain v. Boeing Co., 998 F.2d 68 (2d Cir.1993) (“United Kingdom”). We disagree.
United Kingdom, which involved a three-sided commercial dispute, held that a court hearing a case under the Federal Arbitration Act “cannot consolidate arbitration proceedings arising from separate agreements to arbitrate, absent the parties’ agreement to allow such consolidation.” Id. at 74. United Kingdom rejected as no longer sound some of the reasoning in an earlier decision-Compania Espanola de Petroleos, S.A. v. Nereus Shipping, S.A., 527 F.2d 966 (2d Cir.1975)-which had authorized the consolidation of commercial arbitrations without consent of all parties. See United Kingdom, 998 F.2d at 71.
United Kingdom did not cite CBS-or any labor case for that matter. This is unsurprising, given the distinct bodies of law that govern arbitration in the commercial and labor contexts. United Kingdom ruled on the arbitrability of a commercial dispute under the Federal Arbitration Act; the cases it cited as having undermined our previous rule were all commercial cases construing that Act; and the principle at work was that courts should not read provisions (like three-way arbitration) into negotiated commercial contracts. However, as we learn from United Steelworkers of America v. Warrior & Gulf Navigation Co., 363 U.S. 574, 578-79, 80 S.Ct. 1347, 1351, 4 L.Ed.2d 1409 (1960), a *91collective bargaining agreement is “more than a contract” — another way of saying it is less than a contract. Presumably for that reason, the Supreme Court has deemed commercial arbitration precedent “irrelevant” to cases involving labor arbitration. Id. at 578, 80 S.Ct. at 1351.
Therefore, because commercial arbitration precedents are irrelevant to labor arbitration cases, we conclude that United Kingdom did not overrule CBS by implication and that CBS remains good law. See Emery Air Freight, 23 F.Supp.2d at 320-21; In re Arbitration Between Office & Prof'l Employees Int’l Union & Sea-Land Serv., Inc., No. 96 Civ. 3043, 1998 WL 226160, at *3 (S.D.N.Y. May 5, 1998). But see Active Glass Corp. v. Architectural & Ornamental Iron Workers Local Union 580, 875 F.Supp. 245, 252 (S.D.N.Y.1995) (erroneously holding that United Kingdom overruled CBS), aff'd, 101 F.3d 687 (2d Cir.1996) (unpublished table decision).
C. Discretion
Emery argues that once a court has concluded it has the power to order three-way arbitration, it may not decline to do so. We disagree and conclude that a district court has discretion to grant or deny such relief. See CBS, 414 F.2d at 1329 (after determining that district court had power to order three-way arbitration, reviewing whether “there was a proper exercise of that power”); see also United States Postal Serv. v. National Rural Letter Carriers’ Ass’n, 959 F.2d 283, 286-87 (D.C.Cir.1992) (discussing a “court’s discretion to order tripartite arbitration”); United States Postal Serv. v. American Postal Workers Union, 893 F.2d 1117, 1120 (9th Cir.1990) (“[T]he district court must examine other factors to ensure that tripartite arbitration is a suitable remedy....”).
It remains to be considered whether tripartite arbitration was warranted under these circumstances. - Among factors considered in the cases are (i) the breadth of the relevant arbitration provisions, see CBS, 414 F.2d at 1329; see also United Indus. Workers v. Kroger Co., 900 F.2d 944, 947 (6th Cir.1990); (ii) the existence (or likelihood) of conflicting arbitration awards, cf. CBS, 414 F.2d at 1329; (iii) the compatibility of the arbitration procedures in the two collective bargaining agreements, see CBS, 414 F.2d at 1329; National Rural Letter Carriers’ Ass’n, 959 F.2d at 287; (iv) the retrospective or prospective nature of the awards, see Retail, Wholesale & Dep’t Store Union, Local 390 v. Kroger Co., 927 F.2d 275, 280-81 (6th Cir.1991); and (v) whether the employer should have known of the potential conflict in its incipiency and should have acted to prevent it, see Louisiana-Pacific Corp. v. International Bhd. of Elec. Workers, 600 F.2d 219, 225-26 (9th Cir.1979). Other factors may be relevant, and the district court in this case drew on equitable principles that are apt.
One point of contention among the circuits is the weight to be given to the existence of a previous award issued in an arbitration between two of the parties. In the Ninth Circuit, parties must seek three-way arbitration before any bipartite arbitration proceedings become final. See United States Postal Serv., 893 F.2d at 1121. If an employer waits, even if the employer ends up subject to two conflicting arbitration awards, three-way arbitration will be unavailable. See Louisiana-Pacific Corp., 600 F.2d at 223-26 (citing the “firm federal policy on the finality of a labor arbitrator’s decision”).
This rule has been rejected by two other circuits. See Kroger, 927 F.2d at 280; Local #850, Int’l Ass’n of Machinists & Aerospace Workers v. T.I.M.E.-Dc, Inc., 705 F.2d 1275, 1278 (10th Cir.1983). In Kroger, the district court ordered three-way arbitration after two unions had pursued separate arbitration proceedings that ended with each being awarded the same disputed work. See Kroger, 927 F.2d at 276. Rejecting the Ninth Circuit’s rule barring a tripartite arbitration order in *92such a case, the Sixth Circuit found the situation to be one especially well-suited for the use of this flexible remedy. See id. at 280-82. “[T]he policy of finality with its purpose of achieving a quick and final resolution is not served by separate bipartite awards, neither of which binds all parties concerned.” Id. at 280.2
We decline to follow Louisiana-Pacific. Circumstances could arise in which the later arbitration was not anticipated at the time the first arbitration was conducted, or in which it was unclear at the outset that the remedy or award in the arbitrations would impose conflicting obligations. We prefer a flexible, fact-based approach that affords full play to the discretion and equitable instinct of the district court. The court should certainly consider the federal policy promoting the finality of arbitration awards, see Louisiana-Pacific, 600 F.2d at 223, keeping in mind, however, that this policy may be disserved by irreconcilable awards.
We conclude that the district court did not abuse its discretion in refusing Emery’s request for an order requiring three-way arbitration. The district court observed that the two collective bargaining agreements used incompatible arbitration procedures, and, unlike in CBS, neither union has agreed to follow the procedure in the other union’s agreement. See Emery, 23 F.Supp.2d at 321. The court also found that no “immediate intervention is necessary to keep the peace” because both locals have no-strike provisions in their agreements. Id. In addition, the court noted that it was possible that Local 295’s arbitration would produce a result not in conflict with Local 478’s (i.e., Local 295 could lose). Id.
We see another factor that militated in favor of denying Emery relief. At oral argument, counsel for Local 478 noted that the Teamsters have an internal arbitration process for settling jurisdictional disputes between its locals. Counsel for Emery averred that the company opposed resolving the dispute through this process, in which the employer has no right to participate. It may be, however, that by failing to include Local 295 in the first arbitration — an omission that may be attributable to tactical considerations on Emery’s part or merely a gross oversight — -Emery has dealt itself out of the process.
In any event, since the dismissal of Emery’s complaint was without prejudice, the company may refile its request for three-way arbitration when and if it faces irreconcilable arbitration awards.
CONCLUSION
For these reasons, the judgment of the district court is affirmed.
. Although a nominal defendant, Local 295’s position in the district court aligned it with Emery. Local 295 did not file a brief in Lhis appeal.
. The language of these cases may be more opposed than their holdings, when the holdings are considered in light of the facts. In Louisiana-Pacific, the disputed work had been completed, see 600 F.2d at 220, so the conflicting arbitration awards meant only that the company would face finite liability to one union for past work. In Kroger and T.I.M.E.-Dc, on the other hand, the employer faced conflicting forward-looking awards of disputed work; compliance with both awards was impossible. See Kroger, 927 F.2d at 280-81 (distinguishing Louisiana-Pacific on this basis); T.I.M.E.-Dc, 705 F.2d at 1277 ("T.I.M.E.-DC was, to be sure, faced with inconsistent mandates, veritably on the horns of a dilemma.”). See generally Sherrard L. Hayes, Jr., Comment, The Federal Circuits’ Response to Conflicting Arbitration Awards in Labor Disputes: Split or Harmony Between the Sixth and Ninth Circuits?, 59 Tenn. L.Rev. 353, 363-64 (1992) ("A reasonable middle ground may lie in applying ... Kroger as the rule and Louisiana-Pacific as a carefully carved exception. Louisiana-Pacific could be harmoniously applied only when compliance with apparently conflicting awards remains theoretically possible.”).