Vacated and remanded by published opinion. Judge WILKINSON wrote the opinion, in which Judge SHEDD and Judge AGEE joined.
In this case we must decide when and under what circumstances courts should review a labor arbitrator’s decision. For the reasons given below, we hold that judicial involvement in the labor dispute in this case was premature. Under the complete arbitration rule, the arbitrator should have been given the opportunity to resolve both the liability and remedial phases of the dispute between the Companies and the Union before it moved to federal court. We therefore vacate the district court’s order confirming the merits of the arbitrator’s liability decision and direct that court to return the dispute- to the arbitrator to allow him to rule on the remedial issues and otherwise complete the arbitration task.
I.
The dispute in this case arises out of a 2007 Memorandum of Understanding Regarding Job Opportunities (the “Jobs MOU”) signed by the United Mine Workers of America (the “Union”) and Peabody Coal Company (“Peabody Coal”) as part of a wider collective bargaining agreement. Peabody Coal signed the Jobs MOU on behalf of itself and as a limited agent of its corporate parent, Peabody Holding Com*157pany (“Peabody Holding”), and several of Peabody Holding’s other subsidiaries, including Black Beauty Coal Company (“Black Beauty”). The principal purpose of the Jobs MOU was to require non-unionized companies within the Peabody corporate family to give preferential hiring treatment to coal miners who were either working for or laid off by Peabody Coal. An arbitration clause in the Jobs MOU provided that a “Jobs Monitor” was to resolve any disputes involving the Jobs MOU, and that his decisions would be “final and binding on all parties” to the dispute. J.A. 79. The Jobs MOU was to expire on December 31, 2011.
Later in 2007, Peabody Energy Corporation (“Peabody Energy”), the corporate parent of Peabody Holding and thus the ultimate parent of Peabody Coal and Black Beauty, initiated a spinoff of some of its mining operations to form a new entity called Patriot Coal Corporation (“Patriot”). In conjunction with the spinoff, Peabody Coal became part of Patriot. All but one of the Peabody Holding subsidiaries on whose behalf Peabody Coal had signed the Jobs MOU also became part of Patriot. The one exception was Black Beauty, which, along with Peabody Holding itself, was retained by Peabody Energy. Thus, following the spinoff, Peabody Coal no longer shared any corporate relationship with Peabody Holding or Black Beauty.
In 2008, Black Beauty hired private mine operator United Minerals Company (“United Minerals”) to conduct surface mining on Black Beauty’s property. Black Beauty and United Minerals were non-unionized. United Minerals had no corporate relationship with Peabody Coal and was thus not subject to the Jobs MOU. Shortly after Black Beauty began its work with United Minerals, the Union sent a letter to Peabody Energy and Peabody Holding stating that Peabody Holding and Black Beauty were still bound by the Jobs MOU’s preferential hiring requirements. Peabody Holding disagreed. It took the view that the spinoff of Peabody Coal from the rest of the Peabody corporate family ended any obligation that Peabody Holding or Black Beauty (the “Companies”) had under the Jobs MOU. Because the Union and the Companies could not resolve this dispute among themselves, the Union submitted the dispute to the Jobs Monitor.
The Companies initially argued that the dispute was not even arbitrable under the Jobs MOU’s arbitration clause. It ultimately took a decision from this Court to confirm that the dispute was in fact arbi-trable. Peabody Holding Co. v. United Mine Workers, 665 F.3d 96, 103 (4th Cir.2012). The Union and the Companies thus returned to arbitration to argue the merits of the dispute before the Jobs Monitor.
When the Union and the Companies returned to the Jobs Monitor they decided to bifurcate the dispute. As recounted by the Jobs Monitor in his written decision, the parties asked him to “treat[] in this proceeding solely the question of whether [Peabody Holding] and Black Beauty continued to be bound by the [Jobs] MOU after the ... spinoff.” J.A. 57. The Jobs Monitor noted further that “[i]f that question is resolved in the Union’s favor, and the parties cannot agree on an appropriate remedy for the [Peabody Holding]/Black Beauty refusal to abide by the [Jobs] MOU, resolution of the remedy issue will be submitted to the Jobs Monitor.” J.A. 57.
After receiving arguments from both the Union and the Companies, the Jobs Monitor ruled that the Jobs MOU remained in force even though Peabody Coal no longer had any corporate relationship with Peabody Holding or Black Beauty. The Jobs Monitor then made a few related rulings, *158including that continued enforcement of the Jobs MOU would not run afoul of the National Labor Relations Act (“NLRA”). The Jobs Monitor, however, deferred his decision on one notable issue. During the proceedings, the Companies had argued that Black Beauty’s work with United Minerals was actually exempt from the Jobs MOU by virtue of the fact that Black Beauty had signed its contract with United Minerals before it became bound by the Jobs MOU. The Union responded by noting that even' if Black Beauty’s work with United Minerals was exempt, Black Beauty or Peabody Holding may have contracted for other jobs that should have been covered by the Jobs MOU. The Jobs Monitor determined that he would defer answering this question “until the remedy stage of these proceedings.” J.A. 70. At the conclusion of his decision, the Jobs Monitor stated that he would “retain jurisdiction over this, matter for the limited purpose of resolving any remedial issues on which the parties cannot agree.” J.A. 70.
Unhappy that the Jobs Monitor had found them subject to liability under the Jobs MOU, the Companies sought to vacate the Jobs Monitor’s decision by filing a declaratory judgment action in the Eastern District of Virginia. The Union filed a counterclaim to enforce the decision. The Union also moved to dismiss the Companies’ complaint, arguing that judicial review of the Jobs Monitor’s decision was not proper until arbitration before the Jobs Monitor was complete. Both parties then filed cross motions for summary judgment on the merits of the Jobs Monitor’s liability decision.
The district court denied the Union’s motion to dismiss. It first noted that there was “some disagreement” in the case law as to the nature of the judicial review provision on which the Companies had premised their suit — Section 301 of the Labor Management Relations Act (“LMRA”), 29 U.S.C. § 185(a). Peabody Holding Co. v. United Mine Workers, 41 F.Supp.3d 494, 499 n. 4 (E.D.Va.2014). While some courts describe their jurisdiction under Section 301 as limited to “review of final arbitration awards,” other courts believe Congress conferred “sweeping jurisdiction” under Section 301 and “merely contemplated judicial application of a prudential rule” that would in practice limit review to final awards. Id.
The district court ultimately decided that it did not need to determine if any limitation on judicial review under Section 301 to final awards was jurisdictional strictly speaking or merely prudential. It simply determined that the Jobs Monitor’s “award is final as to liability and therefore reviewable.” Id. The district court reached this conclusion largely because the parties had agreed to bifurcate the liability and remedial facets of their dispute, and the Jobs Monitor’s decision had conclusively resolved the liability facet. Id. at 500-01.
Proceeding to the merits, the district court granted the Union’s motion for summary judgment by enforcing the Jobs Monitor’s decision as to the Companies’ liability under the Jobs MOU. Id. at 507. The Companies timely appealed this order. The Union did not cross appeal the district court’s denial of its motion to dismiss, and instead sought only to defend the district court’s summary judgment order confirming that the Companies were liable under the Jobs MOU. After the parties briefed this question, we asked for additional briefing on whether we should even review the Jobs Monitor’s liability decision in light of the fact that arbitration before the Jobs Monitor was not complete. It is on this threshold question that we now focus.
*159II.
A.
This case came to federal court by way of Section 301 of the LMRA. Section 301 gives federal district courts juris- , diction over “[s]uits for violation of contracts between an employer and a labor organization representing employees in an industry affecting commerce ... without respect to the amount in controversy or without regard to the citizenship of the parties.” 29 U.S.C. § 185(a). Longstanding Supreme Court precedent provides that a party may utilize Section 301 to seek judicial enforcement of an arbitration award made pursuant to an arbitration clause in a collective bargaining agreement. Gen. Drivers Local Union No. 89 v. Riss & Co., 372 U.S. 517, 519, 83 S.Ct. 789, 9 L.Ed.2d 918 (1963) (per curiam). Before a court may review the award, however, it must determine that the award is “final and binding.” Id. In line with this directive, many courts have held that a federal district court should not review a labor arbitrator’s decision under Section 301 until the arbitrator has ruled on both liability and remedies — a procedural requirement commonly referred to as the complete arbitration rule. E.g., Local 36, Sheet Metal Workers Int’l Ass’n v. Pevely Sheet Metal Co., 951 F.2d 947, 949-50 (8th Cir.1992); Union Switch & Signal Div. Am. Standard Inc. v. United Elec. Workers, Local 610, 900 F.2d 608, 612-14 (3d Cir.1990); Millmen Local 550, United Bhd. of Carpenters v. Wells Exterior Trim, 828 F.2d 1373, 1375-76 (9th Cir.1987).
As the district court noted, there appears to be some uncertainty as to the nature of the complete arbitration rule. Some decisions have described the complete arbitration rule as a restriction of a federal court’s jurisdiction under Section 301. Pub. Serv. Elec. & Gas Co. v. Sys. Council U-2, Int’l Bhd. of Elec. Workers, 703 F.2d 68, 70 (3d Cir.1983). But other decisions have noted Section 301’s broad language, and have accordingly taken the complete arbitration rule to be only a prudential limitation on judicial involvement in a labor arbitration. Union Switch, 900 F.2d at 612-14.
Both in briefing and during argument, the Companies claimed and the Union agreed that the complete arbitration rule does not concern federal subject matter jurisdiction in the strict sense. We agree with the parties. Unlike, for instance, 28 U.S.C. § 1291, the statute conferring appellate jurisdiction on the federal circuit courts of appeals, Section 301 itself does not contain language limiting review to a “final decision” or some other similarly definitive event. Its jurisdictional grant is couched in much broader terms. 29 U.S.C. § 185(a).
Indeed, even courts that have referred to the complete arbitration rule in jurisdictional terms appear to acknowledge that it is not a hard and fast jurisdictional limitation, because those courts have noted exceptions to the rule in “extreme cases.” Millmen Local 550, 828 F.2d at 1377. But of course there can be no exception from the fact that federal courts are courts of limited jurisdiction and thus do not have authority to resolve a dispute unless that authority has specifically been given to them. Home Buyers Warranty Corp. v. Hanna, 750 F.3d 427, 432 (4th Cir.2014). All of this is to say that the complete arbitration rule necessarily constitutes only a prudential limitation on a court’s authority to review a labor arbitrator’s decision.
Although only prudential, the complete arbitration rule nonetheless draws from the same well of policy rationales as its strictly jurisdictional relatives. As noted, under 28 U.S.C. § 1291, a district court *160generally must have entered a final judgment or order before a court of appeals can take the case. Goode v. Cent. Va. Legal Aid Soc’y, Inc., 807 F.3d 619, 623 (4th Cir.2015). This requirement “preserves judicial economy by ensuring that a district court maintains authority over a case until it issues a final and appealable order, thus preventing piecemeal litigation and repeated appeals.” Id. at 625.
The complete arbitration rule promotes similar ends. It ensures that courts will not become incessantly dragooned into deciding narrow questions that form only a small part of á wider dispute otherwise entrusted to arbitration. And it mitigates the possibility of one party using an open courthouse door to delay the arbitration. See Union Switch, 900 F.2d at 611. Finally, it makes good sense, when working within a hierarchical system, to give the decision maker at each level a full and fair say as to the whole problem before passing the case on to the next stage of review. Internal appeals in the state and federal courts generally abide by this principle, and there is no reason that it should not operate as a presumptive maxim in this context as well. With this background in mind, we examine why the facts in this case counsel us to adhere to the complete arbitration rule and withhold judicial involvement until the arbitration before the Jobs Monitor is complete.
B.
This case calls for a straightforward application of the complete arbitration rule. As noted, the complete arbitration rule provides that a federal court asked to review an arbitrator’s decision should refrain from doing so until the arbitrator has decided all facets of the dispute. Savers Prop. & Cas. Ins. Co. v. Nat’l Union Fire Ins. Co., 748 F.3d 708, 719 (6th Cir.2014). Accordingly, when a labor arbitrator first decides liability questions and reserves jurisdiction to decide remedial questions at a later time, as appears to be quite common, see Union Switch, 900 F.2d at 611, a federal court should generally withhold review of the arbitrator’s liability decision until the arbitrator has had the opportunity- to rule on the remedial questions as well. See McKinney Restoration Co. v. Ill. Dist. Council No. 1 of Int’l Union of Bricklayers, 392 F.3d 867, 872 (7th Cir.2004); Pub. Serv. Elec. & Gas Co., 703 F.2d at 70.
Here the Jobs Monitor issued a decision as to the liability phase of the parties’ dispute, but retained jurisdiction over the remedies phase should the Union and the Companies fail to agree on a remedy on their own. J.A. 69-70. Because the Jobs Monitor was not finished with the dispute, the complete ' arbitration rule counsels that we refrain from stepping in at this juncture. If this dispute is destined to eventually make its way to court, it is far better for it to come in one whole piece than in dribs and drabs.
The Companies argue, however, that application of the complete arbitration rule to this case is not so straightforward, and offer reasons why we should review the merits of the Jobs Monitor’s liability decision. First among those reasons is that the Companies and the Union chose to bifurcate their dispute into separate liability and remedial proceedings. The Companies highlight decisions permitting judicial review of a labor arbitrator’s liability decision when the parties decide beforehand to deal separately with the liability and remedial aspects of their dispute. Smart v. Int’l Bhd. of Elec. Workers, Local 702, 315 F.3d 721, 726 (7th Cir.2002); Providence Journal Co. v. Providence Newspaper Guild, 271 F.3d 16, 19-20 (1st Cir.2001).
*161It is true that the parties agreed to bifurcate their dispute into two proceedings, one to address liability, and one to address remedies, if necessary. Given the nature of the dispute, this seems like a sensible approach. It is unsurprising that the parties could not find common ground on the question of whether the Jobs MOU survived the spinoff — -this is a zero sum liability question on which neither party would want to give in. No doubt, though, the parties at least contemplated the possibility of some compromise as to the remedies question once they received a definitive answer as to liability. One of the many virtues of arbitration is that parties can segment the dispute resolution process in a manner that enhances the prospects for settlement.
That the parties agreed to bifurcate their arbitration proceedings does not change the fact that they also agreed to submit the entire dispute — both the liability and remedies questions — to arbitration. The arbitration clause in the Jobs MOU provides that “[a]ny dispute alleging a breach of th[e] [Jobs] MOU” may be submitted to the Jobs Monitor for resolution. J.A. 79. And it is clear from the Jobs Monitor’s written decision that the “matter” given to him by the parties included both the liability and remedial facets of the dispute. J.A. 57. For understandable reasons, the parties asked the Jobs Monitor to deal with each question in a separate “proceeding.” J.A. 57. That is, the parties gave the Jobs Monitor one large task, and then asked him to deal with that task in a specific, segmented manner. There is nothing unjust about a decision to withhold review until the arbitrator has completed both segments of the whole task that was given to him.
The Companies also argue that we should proceed to the merits because it would be more efficient to have judicial review now rather than later. The Companies essentially contend that it would be a waste of resources to force the parties to proceed through the remedial phase of the arbitration if the Companies’ position on the liability question is eventually determined by a court to be correct. This argument sweeps too broadly. It could in principle be applied to all but the simplest cases, because it could always be claimed that judicial review of an arbitrator’s liability ruling might potentially save the parties and the arbitrator remedial time. In fact, the Companies’ argument could even be used to support one party’s right to claim immediate recourse to court in disputes where there is no semblance of bifurcation.
Moreover, the Companies’ efficiency argument overlooks the widely held view that the sort of interlocutory appeal the Companies are requesting can, if not circumscribed, become “inherently ‘disruptive, time-consuming, and expensive.’ ” Prado-Steiman ex rel. Prado v. Bush, 221 F.3d 1266, 1276 (11th Cir.2000) (quoting Waste Mgmt. Holdings, Inc. v. Mowbray, 208 F.3d 288, 294 (1st Cir.2000)). One notable reason interlocutory appeals tend to reduce rather than promote efficiency is that they often “require[] the appellate courts to consider issues that may be rendered moot if the appealing party ultimately prevails in or settles the case.” Id.
Were we to review the merits of the liability decision now, we may end up considering an issue later rendered moot. As noted, the Jobs Monitor has yet to decide if Black Beauty’s work with United Minerals is exempt from the Jobs MOU. And as far as we are aware, Black Beauty’s work with United Minerals is the only potential breach of the Jobs MOU that the Union has thus far identified. If, therefore, the Jobs Monitor finds that Black Beauty’s work with United Minerals is exempt, and *162if the Union does not identify other potential breaches of the Jobs MOU, then our review of the liability decision will have had no practical impact on the parties’ dispute. And no matter what the Jobs Monitor might do during the remedial phase, settlement is always a possibility. Dollars and cents are fertile subjects for compromise. Having lost on the liability question, the Companies may decide to negotiate an alternative jobs agreement or reach some other monetary agreement with the Union.
In addition, the Companies’ efficiency argument is undercut by the particularized nature of this dispute. It is not as if a court ruling on the liability question now would settle a common issue for multiple cases proceeding simultaneously before different arbitrators. The liability question is instead of concern only to Peabody Holding and Black Beauty.
And even if a court ruling at this juncture would in some way advance systemic efficiency, we would hesitate to make such a ruling in light of the fact that the Jobs Monitor’s decision on the liability question will not have any real-world effect until either the parties or the Jobs Monitor decide on a corresponding remedy. One rationale that has been given for allowing a court to review an arbitrator’s liability decision in a bifurcated arbitration is that the liability decision was “expressly intended to have immediate collateral effects” in another proceeding. Trade & Transp., Inc. v. Nat. Petroleum Charterers Inc., 931 F.2d 191, 195 (2d Cir.1991). But the Companies have identified no similar adverse consequences here. That the Jobs Monitor’s decision has no such immediate impact bolsters our decision to withhold judicial review in this case.
Finally, the Companies’ whole line of argument for immediate judicial review runs awkwardly into a first principle of arbitration: that “arbitration is a matter of contract.” Am. Exp. Co. v. Italian Colors Rest, — U.S. -, 133 S.Ct. 2304, 2309, 186 L.Ed.2d 417 (2013). Because arbitration is contractual in nature, parties to an arbitration agreement are generally free to fashion the arbitral process to best suit their needs. See Vulcan Chem. Techs., Inc. v. Barker, 297 F.3d 332, 340 (4th Cir.2002). For instance, they may agree among themselves which questions will go to arbitration, which law the arbitrator will apply in the arbitration, and which procedural rules the arbitrator will use to manage the arbitration. The agreement fashioned by the parties deserves judicial respect. Here, we have done nothing more or less than honor the arbitral ground rules the Companies and the Union have established for themselves.
III.
Arbitration plays a critical role in our nation’s system of labor relations. By providing a forum in which labor and management can meet to peaceably resolve their differences, labor arbitration serves as a “substitute to industrial strife.” Gateway Coal Co. v. United Mine Workers, 414 U.S. 368, 378, 94 S.Ct. 629, 38 L.Ed.2d 583 (1974) (quoting United Steelworkers v. Warrior & Gulf Nav. Co., 363 U.S. 574, 578, 80 S.Ct. 1347, 4 L.Ed.2d 1409 (1960)). For this reason, Congress has adopted a “federal policy favoring arbitration of labor disputes.” Granite Rock Co. v. Int'l Bhd. of Teamsters, 561 U.S. 287, 299, 130 S.Ct. 2847, 177 L.Ed.2d 567 (2010) (quoting Gateway Coal Co. 414 U.S. at 377, 94 S.Ct. 629). The Companies have given us no reason to disrespect the important place that labor arbitration occupies in our economy by intervening prematurely and hearing this dispute before the arbitrator has completed his job. We therefore vacate the district court’s ruling and direct that *163court to remand this case to the Jobs Monitor for further proceedings.
VACATED AND REMANDED