MEMORANDUM AND ORDER ON EMERGENCY MOTIONS TO ENFORCE THE COURT’S PRIOR RULING AND TO IMPOSE SANCTIONS
This dispute arises over respondent First State Insurance Group’s (First State) relentless insistence that its multi-contract dispute with petitioner Employers Insurance of Wausau (Wausau), should be consolidated for arbitration before a single panel of the American Arbitration Associa*335tion (AAA). The essential background is as follows. On October 16, 2002, First State brought an action in the federal district court against Nationwide Mutual Insurance Co. (Nationwide), docketed as 02-12012-RGS, seeking to compel the arbitration of a dispute over the parties’ obligations under five reinsurance contracts. On November 18, 2002, Wausau, which was involved in a similar dispute with First State over four such contracts, filed a preemptive action, docketed as 02-12252-RGS, asking that the court stay proceedings then pending before the AAA and appoint separate arbitrators for each contract.1 First State opposed the stay and moved for an order consolidating the disputes for arbitration. On December 17, 2002, after a hearing, the court ruled orally on the relief requested by all parties, denying Wausau’s and Nationwide’s motion for a stay, allowing First State’s motion to compel, but denying, reluctantly,2 its motion to consolidate.3 According to the Clerk’s notes, the court had this to say about the consolidation issue.
After hearing, the court ruled orally that: the contracts between the parties are separate and singular. That as a result either party is entitled to insist on four (4) separate arbitrations. There is no language in any of the contracts permitting the inference that the parties agreed to consolidation of the contracts for purposes of arbitration, this issue is therefore not arbitratable. The thirty (30) days contemplated by the contracts for the arbitrators to agree to a neutral umpire commences running as of today. If the parties’ arbitrators cannot agree, the selection of umpires is to be made by the AAA as the contracts require and any issue as to the rules by which the arbitration is to proceed is not properly before the court.4
So matters stood until Wausau brought to the court’s attention the fact that First State had petitioned the AAA for the appointment of a single arbitration panel, with its counsel representing to the AAA that “a federal court has already ruled against Wausau in its erroneous contention that there must be different umpires for each of these proceedings.” In light of the mischaracterization of its ruling, on May 7, 2003, the court held a hearing on Wausau’s motion that First State be held in contempt. At the hearing, the following ex*336change occurred between the court and First State’s attorney.
The Court: My ruling was, though, that they were entitled to insist on four [arbitrators]. I counseled them to choose one.
Mr. Gura: If they didn’t — -are you saying that there could be — you ordered there were four separate umpires? There had to be four separate umpires?
The Court: Of course I did. That is exactly — I said that was my interpretation of the contract. I do not see how the transcript could be read to [support] any other conclusion.
That is what I ruled. I did not rule against Wausau. I ruled for Wausau.
Mr. Gura: And, your Honor, the AAA — the AAA process, your Honor, selects the umpires. We can’t tell the — we -
The Court: I care not for the AAA process. I want to know why you were writing a false statement to the American Arbitration Association about a ruling I made?
Mr. Gura: Because I don’t believe, your Honor, when I read the transcript that that, in fact, was your ruling, your Honor. I believe in reading this last sentence, umpire or umpires, as the case may be, the parties could - The Court: Please. That would not fly even in law school. Read the context.
Despite the court’s evident pyrrhonism, it yielded to Mr. Gura’s proffered excuse that he had been confused by the ruling. Consequently, the court denied the motion for sanctions. The parties then returned to arbitration. Separate panels were appointed and the proceedings began their usual course. Believing the matter resolved, on March 18, 2003, the court dismissed the case and terminated the docket.
Unmentioned at the May 17, 2003 hearing was a pertinent Court of Appeals decision, Shaw’s Supermarkets, Inc. v. United Food and Commercial Workers Union, Local 791, 321 F.3d 251 (1st Cir.2003), which had been handed down on March 6, 2003. In Shaw’s, the plaintiff supermarket objected to an order of the district court requiring it to arbitrate grievances that had arisen under three separate collective bargaining agreements, and to submit the issue of consolidation to the arbitrators.5 The supermarket appealed, arguing that consolidation is an issue of substantive ar-bitrability, and not a question of procedure, and the issue was therefore for the court and not the arbitrator to decide. The Court of Appeals disagreed.
The issue before us is who should make the determination as to whether to consolidate the three grievances into a single arbitration: the arbitrator or a federal court. Since each of the three grievances is itself concededly arbitra-ble, we think the answer is clear. Under Howsam v. Dean Witter Reynolds, Inc., 537 U.S. 79, 123 S.Ct. 588, 154 L.Ed.2d 491 (2002), this is a procedural matter for the arbitrator.
Shaw’s, 321 F.3d at 254.
Despite the import of Shaw’s, First State made no request that the court vacate or reconsider its ruling on the consolidation issue. Rather, a year later, on May 28, 2004, First State moved again before the AAA to consolidate the three *337remaining Wausau arbitrations (and the five Nationwide arbitrations), informing the existing panels that in light of the Shaw’s decision, “the December 17, 2002 decision of U.S. District Court Judge Richard Stearns holding that the issue of consolidation is ‘not arbitrable,’ is wrong under the current state of the law, and therefore, not binding.” First State further advised the panels that because the district court’s decision to deny its motion to consolidate was a “nullity,” only they, “and not any court,” possessed the power to correct the district court’s “judicial error.”
While First State may be correct in its assessment of the holding in Shaw’s, its exhortation to panels of private arbitrators to take it upon themselves to unilaterally overturn a district court’s ruling on a matter of law, is very troubling. It is the office of an Article III Court of Appeals, and not that of private litigants or arbitrators, to correct errors of law committed by an Article III district court. “[A] realistic concern for the finality and integrity of judgments would arise if parties were free to ignore federal court decisions that conclusively settled claims or issues now sought to be arbitrated.” John Hancock Mut Life Ins. Co. v. Olick, 151 F.3d 132, 138 (3d Cir.1998).
The power of a federal court to enforce adherence to its lawful rulings is not only well-established but essential to the functioning of the judicial system. In Y & A Group Securities Litig., 38 F.3d 380 (8th Cir.1994), Valk, a disappointed investor, brought arbitration proceedings against his brokerage firm. When the arbitration panel denied the firm’s motion to dismiss, the firm repaired to the district court, which promptly enjoined the arbitration as contrary to its prior approval of a consent judgment involving the original stock-touting scheme.
[FJederal “[c]ourts should not have to stand by while parties re-assert claims that have already been resolved.” Kelly v. Merrill Lynch, Pierce, Fenner & Smith, 985 F.2d 1067, 1069 (11th Cir.), cert. denied, 510 U.S. 1011, 114 S.Ct. 600, 126 L.Ed.2d 565 (1993). No matter what, courts have the power to defend their judgments as res judicata, including the power to enjoin or stay subsequent arbitrations.
The All Writs Act makes plain that each federal court is the sole arbiter of how to protect its own judgments: federal courts “may issue all writs necessary ... in aid of their respective jurisdictions....” 28 U.S.C. § 1651(a). It is this concept that underlies the related rule that the court which issues an injunction is the only one with authority to enforce it. Klett v. Pim, 965 F.2d 587, 590-91 (8th Cir.1992).
Valk is thus incorrect in arguing that the district court is precluded from reconsidering the arbitration panel’s denial of Dean Witter’s motion to dismiss. After all, this denial is based on the panel’s interpretation of the settlement agreement incorporated in the district court’s final judgment. The district court, and not the arbitration panel, is the best interpreter of its own judgment.
Id. at 382-383.
Whether the court’s ruling in this case, as opposed to the consent decree in the Y & A case, had sufficient finality to be cloaked with the doctrine of res judicata, as Wausau argues it does, is not an issue that need be decided.6 But see Seguro de *338Servicio de Salud de Puerto Rico v. McAuto Systems Group, Inc., 878 F.2d 5, 8 n. 3 (1st Cir.1989) (orders resulting from proceedings to compel and consolidate ar-bitrations are to be deemed “final”). At a minimum, as First. State concedes, the court’s December 17, 2002 ruling constituted the law of the case. While it is true, as First State argues, that the law of the case doctrine does not prevent a reexamination of a court’s rulings in the wake of subsequent developments in the law, it is the court, not the parties, to which the power to conduct such a reexamination is committed. “We have ... recognized that a district court may, as an exception to the law of the case doctrine, reexamine a previous ruling when ‘controlling authority has since made a contrary decision of the law applicable to such issues CPC International, Inc. v. Northbrook Excess & Surplus Ins. Co., 46 F.3d 1211, 1215 (1st Cir.1995) (emphasis added).
To be sure, the law of the case doctrine is neither an absolute bar to reconsideration nor a limitation on a federal court’s power. See White v. Higgins, 116 F.2d 312, 317 (1st Cir.1940); see also Morgan v. Burke, 926 F.2d 86, 91 (1st Cir.1991) (warning against “transforming] ‘law of the case’ into a ... straitjacket for a court”). Nonetheless, this modicum of residual flexibility does not mean that the doctrine can. — or should — be lightly shrugged aside. To the contrary, the doctrine is a salutary rule of policy and practice, grounded in important considerations related to stability in the decisionmaking process, predictability of results, proper working relationships between trial and appellate courts, and judicial economy. The law of the ease should be treated respectfully and, in the absence of exceptional circumstances, applied according to its ten- or.
United States v. Rivera-Martinez, 931 F.2d 148, 150-151 (1st Cir.1991).
The appropriate means of prompting a change or a modification in a court’s ruling is by the filing of a prompt petition for reconsideration or for relief from judgment pursuant to Rule 60(b). See United States v. DeJesus, 752 F.2d 640, 643 (1st Cir.1985) (per curiam). The inappropriate means is by a resort to self-help, particularly when it involves an incitement to disobedience of a court’s ruling. As Wausau accurately characterizes it, First State’s course of conduct has been both inexcusable and incomprehensible.
Given its reliance on Shaw’s Supermarkets as the subsequent authority that purportedly warrants the removal of the law of the case barrier, First State should have moved this Court for a reconsideration promptly after March 6, 2003, instead of letting this case go to closure and proceeding with the empaneling of four separate arbitration panels, participating in the organizational meetings and actively conducting four separate arbitrations, only to inexplicably and inexcusably spring its motions more than a year later and in the arbitrations instead of this Court.
Wausau Brief, at 12-13.7 See also North River Ins. Co. v. Philadelphia Reinsur*339ance Corp., 63 F.3d 160, 165-166 (2d Cir.1995).
ORDER
For the foregoing reasons, the emergency motions of Wausau and Nationwide are ALLOWED in part. First State is hereby ORDERED to withdraw forthwith its motions for consolidation pending before the arbitration panels. It is further ORDERED that First State pay such costs and attorneys’ fees as have been incurred by Wausau and Nationwide in bringing these motions in a reasonable amount to be determined by the court on the parties’ submissions.
SO ORDERED.