Affirmed by published opinion. Senior Judge HAMILTON wrote the opinion, in which Chief Judge HILTON joined. Judge TRAXLER wrote a dissenting opinion.
OPINION
HAMILTON, Senior Circuit Judge.
The United States District Court for the District of Maryland enjoined a husband [430]*430and wife, both citizens of California, from seeking enforcement of a multi-million dollar arbitration award for legal malpractice that the couple had obtained in California against their former attorney, who was also a citizen of California. In entering its injunction (the Injunction), the district court relied upon the All Writs Act, 28 U.S.C. § 1651(a), which provides that “[t]he Supreme Court and all courts established by Act of Congress may issue all writs necessary or appropriate in aid of their respective jurisdictions and agreeable to the usages and principles of law.” Id. The district court believed the Injunction was necessary “to protect the integrity of [its] processes and prevent the Honda [multi-district litigation] proceedings [that had been before it] from being used for an improper purpose....” In re: American Honda Motor Co., Inc. Dealerships Relations Litig., 162 F.Supp.2d 387, 396 (D.Md.2001).
The couple are parties to a multi-district litigation (MDL) settlement agreement that was formally approved by the district court and over which the district court expressly retained exclusive jurisdiction to rule upon interpretive questions. The district court found the couple had intentionally misled the California arbitrator about the actual nature of the MDL proceedings, and that the couple had knowingly and im mtionally pressed an argument before the arbitrator that necessarily required the arbitrator to resolve a significant interpretive question involving substantive provisions of the MDL settlement agreement.
For reasons that follow, we affirm the district court’s order entering the Injunction.
I.
The couple to which we have just referred are Ruth and Roger Miller (the Millers).1 At the end of 1986, the Millers purchased Huntington Beach Honda Automobile Dealership, partly through owner financing. The Millers later defaulted on their financing obligations under the purchase deal, and as a result, the widow of one of the two former owners of the dealership filed a civil action against the Millers in California state court in March 1994 (the 1994 State Court Action). The Millers, who were not then represented by legal counsel, filed a cross-complaint, and joined the widow of the other former owner as a defendant on the cross-complaint.
In July 1994, California attorney Lawrence Silver (Silver) undertook legal representation of the Millers in the 1994 State Court Action. In this regard, Silver and the Millers entered into a retainer/fee agreement for legal services, under which Silver and the Millers agreed that any disputes between them “shall be subject to mandatory arbitration.” (J.A. 587).
In April 1995, Silver filed an amended cross-complaint on behalf of the Millers naming American Honda Motor Company, Incorporated (American Honda) as a defendant, asserting claims against the company under the Racketeer Influenced and Corrupt Organizations Act (RICO), 18 U.S.C. § 1961 et seq., and under California common law. All such claims arose from the Honda bribery scandal that eventually became the subject of the MDL proceedings before the district court in Maryland (the Honda MDL Proceedings).2 The crux of the bribery scandal was that Honda received kickbacks and bribes from certain [431]*431Honda dealerships throughout the United States in return for increased allocations of selective new cars.
American Honda filed a demurrer to the RICO claim in the Millers’ amended cross-complaint, in the 1994 State Court Action, on the ground that the Millers had failed to plead legally sufficient damages under RICO. The demurrer was sustained without leave to amend, but without prejudice to the Millers’ ability to file a motion to reconsider the court’s decision denying leave to amend. In accordance with this order, Silver, on behalf of the Millers, filed a motion for reconsideration, which was denied.
The relationship between the Millers and Silver subsequently deteriorated, and after the Millers threatened to assert claims for legal malpractice against Silver, Silver withdrew his appearance as counsel for the couple in the 1994 State Court Action. Thereafter, against Silver’s advice, the Millers voluntarily dismissed their remaining claims in the 1994 State Court Action and refiled them in the United States District Court for the Central District of California. The Millers’ claims were then transferred to the district court (for the District of Maryland) as part of the Honda MDL Proceedings. Once the Millers’ claims became part of the Honda MDL Proceedings, Honda moved to dismiss them on the basis that the Millers’ voluntary dismissal of those same claims in the 1994 State Court Action constituted dismissal with prejudice.
The law firm of Duane, Morris & Heckscher (Duane/Morris) represented the Millers as well as several other plaintiffs in the Honda MDL Proceedings. Members of Duane/Morris served on the plaintiffs’ executive committee, and the Millers personally participated in the settlement approval process. Ultimately, the Millers opted to accept the settlement agreement which concluded the Honda MDL Proceedings. Hereafter, we will refer to this settlement agreement as “the MDL Settlement Agreement.” Under the MDL Settlement Agreement, the Millers received the largest amount of damages of any dealership — $6.32 million. But according to the district court’s memorandum opinion that accompanied its injunction order presently under review, $6.32 million “was $1 million too high under the allocation formula that was used in determining the amounts to be paid to settling class members.” In re: American Honda, 162 F.Supp.2d at 389. In this regard, the district court explained as follows:
The formula contemplated that each dealer would be paid $4,000 for each car which, as determined by a regression analysis, the dealer had not received because of the bribery scheme. Some dealers, like the Millers, purchased their dealership during the class period, and were entitled to compensation only for those cars that were apportioned under the settlement formula to the dealership after the date of their purchase. This apportionment ordinarily was easy to accomplish because — apparently in all cases other than the Millers — Honda assigned a new dealer number when the dealership changed hands. The Millers, however, were given the same dealer number as their predecessors and therefore received an apportionment of all of the cars to which their dealership was entitled in 1986 despite the fact that they did not purchase the dealership until mid-December of that year. This resulted in a misapportionment to them of 250 cars, which in turn resulted in an excess recovery of $1 million. The error apparently was known both to the Millers and Duane/Morris when the Millers decided to accept the MDL settlement.
Id. at 389-390 (emphasis added).
In March 1997, the Millers sued Silver for legal malpractice in California state [432]*432court. The Millers alleged that Silver had acted negligently in the 1994 State Court Action. The parties subsequently agreed that the malpractice action would be dismissed without prejudice and that the statute of limitations would be tolled until April 1999.
On October 9, 1998, the district court entered its “Order of Final Settlement Approval and Judgment of Dismissal of Settled Claims” in connection with the MDL Proceedings.3 In this order, the district court formally approved the MDL Settlement Agreement. In so approving, the district court expressly found that the total amount of settlement to be paid the plaintiffs’ class under the MDL Settlement Agreement was “fair, reasonable, and adequate, and in the best interests of [the] Plaintiff[s’] Class as a whole.” (J.A. 548). Likewise, the district court found that the plan of distribution to individual class members under the MDL Settlement Agreement was “fair and reasonable, [and] is in the best interest of the Plainti£f[s’] settlement class.... ” (J.A. 550). Of significant relevance in the present appeal, the district court’s Settlement Approval Order states that the district court “shall have and retain exclusive jurisdiction with respect to (i) implementation, interpretation and enforcement of the Settlement Agreement; (ii) supervision, allocation and distribution of the settlement fund; and (iii) any applications or disputes concerning attorneys’ fees, costs, and expenses which may arise.” (J.A. 551).
After the district court entered its Settlement Approval Order, Silver filed a notice of lien in the district court against the Millers’ share of the settlement proceeds. Silver based his lien upon his claim that he deserved compensation for the work that he had performed for the Millers in the 1994 State Court Action.
On the eve of expiration of the tolling agreement between the Millers and Silver, the Millers filed a malpractice action against Silver in California state court (the 1999 State Court Action). In their complaint, the Millers acknowledged that they had partially mitigated their damages through the MDL Settlement Agreement. Nevertheless, the Millers alleged that but for Silver’s negligence, they would have recovered an additional $7 million in connection with the Honda bribery scheme. Silver filed a counterclaim for approximately $1.8 million in attorney’s fees.
Silver next made a motion before the district court requesting that the district court adjudicate the merits of his lien against the Millers’ share of the proceeds under the MDL Settlement Agreement. He concomitantly requested that the district court adjudicate the merits of the Millers’ malpractice claim against him pending in the 1999 State Court Action and his counterclaim for attorney’s fees in the same action.
The Millers vehemently opposed the motion on the ground that California state law issues would predominate in their dispute with Silver. Notably, as found by the district court, the Millers did not disclose before the district court that they intended to assert a legal malpractice theory in the 1999 State Court Action that would require an intimate knowledge of the legal issues involved in the Honda MDL Proceedings and the MDL Settlement Agreement. They also did not disclose before the district court that they intended to argue in such action that the damages they were seeking from Silver were distinct [433]*433from the damages due them under the MDL Settlement Agreement.
Based upon the Millers’ representation that issues of California state law would predominate in all of the disputes between themselves and Silver, the district court initially declined to exercise jurisdiction to adjudicate the merits of Silver’s lien against the settlement proceeds due the Millers under the MDL Settlement Agreement, as well as the merits of the Millers’ malpractice claim against Silver in the 1999 State Court Action and his counterclaim for attorney’s fees.
Having lost his motion to have the district court adjudicate the merits of his malpractice/fee dispute with the Millers, Silver relied upon the mandatory arbitration provision in the retainer/fee agreement between himself and the Millers to move in the 1999 State Court Action for mandatory arbitration. The California state court granted the motion.
The arbitration, which lasted a total of fifteen days, took place in California before a retired California state court judge. A key issue in the arbitration was whether, but for Silver’s alleged negligence, the Millers would have obtained a greater recovery from American Honda in the 1994 State Court Action than they did under the MDL Settlement Agreement. Of relevance on appeal, the Millers contended that, if their case had been handled properly, they would have recovered $7,475,000 in so-called “blue sky damages’! from American Honda for having greatly overpaid for goodwill at the time they purchased their dealership. The Millers denied before the arbitrator that the MDL Settlement Agreement compensated them for such “blue sky damages.” The Millers referred to the damages due them under the MDL Settlement Agreement as “allocation damages.” According to the Millers, these damages only compensated them for their lost profits as a result of not receiving their fair allocation of automobiles from Honda.
On January 10, 2001, the arbitrator issued an award heavily in favor of the Millers. Finding that the MDL Settlement Agreement did not compensate the Millers at all for the amount they had overpaid in goodwill when they purchased their dealership, the arbitrator awarded the Millers $7,475,000 as damages for such overpayment.4 The arbitrator declined to award the Millers any amount of “allocation damages” on the basis that the Millers were awarded an adequate amount of “allocation damages” under the MDL Settlement Agreement. The arbitrator ruled against Silver on his counterclaim for attorney’s fees. In a supplemental award issued at a later date, the arbitrator awarded the Millers $871,474.96 in attorney’s fees in connection with their prosecution of their malpractice claim.
After issuance of the'arbitration award, Silver filed a motion in the Maryland district court for reconsideration of the district court’s decision not to adjudicate the merits of his malpractice/fee dispute with the Millers. Silver also sought a permanent injunction to enjoin the Millers from enforcing their arbitration award in California .state, court. , The.-parties fully briefed and argued the motion before the district court, and the Millers agreed not to seek judicial enforcement of their arbitration award pending a decision by the district court.
On August 24, 2001, the district court issued an order and memorandum opinion granting Silver’s motion and permanently enjoining the Millers from enforcing their [434]*434arbitration award to the extent that it awarded them $7,475,000 for so-called “blue sky damages.” In re: American Honda, 162 F.Supp.2d at 387-396. The district court also enjoined the Millers from enforcing the supplemental award of attorney’s fees with the proviso that the Millers had the opportunity to file a motion with the district court for a determination regarding the amount of attorney’s fees and costs that they had incurred in the arbitration proceedings in connection with their “blue sky damages” claim. Id. at 396. The district court ruled that after determining such amount, it would modify the Injunction to permit the Millers to enforce the remaining portion of the supplemental award. Id.
Because we review on appeal the district court’s entry of the Injunction for abuse of discretion, In re March, 988 F.2d 498, 500 (4th Cir.1993), we will next set forth the district court’s expressed reasons for entering the Injunction. The district court began the analysis portion of its August 24, 2001 memorandum opinion by setting forth the Millers’ first theory as to why the district court should not enter the Injunction. In this regard, the district court stated as follows:
The theory espoused by the Millers during the arbitration proceedings in support of their claim for blue sky damages was relatively straightforward. According to the Millers, [the judge in the 1994 State Court Action] had sustained Honda’s demurrer in the litigation ... because Silver had misplead RICO damages by not claiming “concrete financial loss” as required by the decision in Sheperd v. American Honda Motor Co., 822 F.Supp. 625 (N.D.Cal.1993). Further, according to the Millers, Silver knew how to plead damages properly because in the case of Austin Motors v. American Honda, which he filed on behalf of other clients in the Central District of California and which was transferred here as a part of the MDL proceedings, I overruled a motion to dismiss filed by the Honda defendants on Sheperd grounds. The sustaining of the demurrer in the California case led to the Millers’ decision to dismiss that action. That dismissal, in turn, led to the motion to dismiss the Millers’ claims filed by Honda in this court. Honda’s motion was still pending before me when the MDL settlement was reached, and the Millers assert that their fear that I would grant the motion lead them to accept the settlement instead of opting out. Finally, they contend, that if they had opted out, they would have pursued their case against Honda and received both the allocation damages they received as part of the MDL settlement and the blue sky damages they allegedly suffered as a result of having overpaid for their dealership.
In re: American Honda, 162 F.Supp.2d at 390-91 (footnote omitted).
The district court identified what it believed to be five flaws in the Millers’ causation theory. The first flaw the district court identified was that no one familiar with the Honda bribery scheme litigation could reasonably conclude that Silver’s alleged malpractice in not pleading RICO damages properly in the 1994 State Court Action is what caused the state court judge to sustain Honda’s demurrer. The second flaw the district court identified was that even assuming that Silver misplead the RICO damages in the 1994 State Court Action, that misfeasance was not the precipitating event which allegedly placed the Millers on the horns of a dilemma in deciding whether to accept the MDL Settlement Agreement. Rather, the district court reasoned, “their predicament was caused by their voluntary dismissal of the California action after Silver no longer represent[435]*435ed them and against his advice.” Id. at 392.
The third flaw the district court identified in the Millers’ causation theory was that, to the extent the Millers prompted the arbitrator to award them so-called “blue sky damages” by arguing that such damages were something different than “allocation damages,” the Millers caused the arbitrator to usurp the district court’s exclusive jurisdiction to interpret the MDL Settlement Agreement. With regard to the merits of the interpretive issue itself, the district court held that the Millers’ argument was off the mark, reasoning as follows:
As I have earlier indicated, the blue sky damages award was intended to compensate the Millers for overpaying ... for the goodwill of their dealership. Goodwill had been calculated for purposes of the purchase agreement as a multiple of the dealership’s prior earnings. Its value was found by the arbitrator to have been inflated because the earnings on which it was based were themselves inflated by the sale of cars that had been allocated to the dealership by corrupt Honda executives in return for bribes that [the previous owners] had paid. Although the damage for overpayment of , goodwill is somewhat conceptually different from damages that the Millers suffered by misallocation of automobiles to them after they had purchased the dealership, the two types of damage are economically interrelated. From one perspective, the recovery the Millers received through the MDL settlement for automobiles they should have received but for the bribery scheme substantially compensated them for the full revenue stream for which they had paid when they purchased the dealership. In any event, economics aside, the settlement agreement in the MDL settlement defined “allocation claims” to encompass “any claim, allegation or assertion arising in any way from the allocation or distribution of Honda automobiles.... ” Under this definition the blue sky damages the Millers received in the arbitration proceeding clearly were not distinct from, but one of the aspects of, allocation damages.
Id. at 393 (second ellipses in original).
The fourth flaw the district court identified in the Millers’ causation theory was that the Millers received $1 million more under the MDL Settlement Agreement than they were actually entitled to for allocation damages as the Millers restrictively define it, yet the Millers faded to disclose such overpayment to the arbitrator. The fifth and final flaw in the Millers’ causation theory identified by the district court was that in awarding the Millers so-called “blue sky damages,” the arbitrator made a speculative assumption that the Millers would have recovered “blue sky damages” in state court if they had not accepted the MDL Settlement Agreement.
The district court next addressed the Millers’ argument that however great the injustice their fallacious arguments in the arbitration proceeding may have created, the district court was powerless to remedy it because of the strong federal policy in favor of arbitration, and because the district court lacked jurisdiction to review an arbitration award entered in a California state proceeding. In response, the district court acknowledged that the general propositions of law upon which the Millers relied were sound, but stressed that this case “turns not upon general principles but on its particulars.” Id. at 395. The district court then went on to state:
Were I not to grant relief to Silver, I would be permitting the MDL proceedings over which I presided to become a vehicle for the commission of a substantial injustice. The Millers actively participated, both through their counsel and [436]*436in a pro se capacity, in the MDL proceedings. They received a substantial settlement from it, including $1 million more than they were entitled to under the allocation formula. They knew that in order to approve the settlement, I would have to find that it was “fair, adequate and reasonable” for all members of the class, including persons, such as themselves, who had allegedly overpaid for their dealerships because of the bribes paid by their predecessors. They never disclosed at the time they accepted the settlement their own view that the settlement was, in fact, unfair, inadequate, and unreasonable because it did not compensate them and similarly situated class members for their blue sky damages. Nor did they reveal that they were reserving their right to pursue such a claim against their former attorney.
Moreover, when opposing Silver’s original motion requesting that I exercise jurisdiction over this dispute, the Millers misrepresented that issues of state law would predominate in resolution of the dispute. They did not disclose that they would be asserting in the arbitration proceeding a legal malpractice theory that would require an intimate knowledge of the legal issues involved in the Honda MDL proceedings. They also did not reveal that one of the contentions they intended to make in the arbitration proceeding was that the blue sky damages they were seeking were distinct from the allocation damages they had recovered in the MDL settlement. Resolution of that issue involved interpretation of the MDL settlement agreement and, as the Millers knew, the settlement agreement conferred exclusive jurisdiction upon this court to interpret its terms.
Most importantly, for the reasons I have previously stated, the Millers made arguments before the arbitrator about the Honda-related litigation that were so totally without merit that they can only be characterized as untrue. They also withheld from the arbitrator that they received $1 million for 250 cars apportioned to them before they purchased their dealership.
Id. at 395-96. In a footnote, the district court added that it was enjoining the arbitration award “not because of any mistake [the arbitrator] made but because the Millers had no right to make before him the deceptive arguments they did, misrepresenting what had occurred during the Honda bribery litigation.” Id. at 395 n. 7.
To summarize, the district court viewed “the global settlement of the claims arising from the Honda bribery scheme [ ]as an asset, both financial and judicial in nature, created under the auspices of the MDL proceedings.” Id. at 396. The district court believed that “[t]hose who accepted its benefits have no right to obtain further recovery (either from Honda or any third parties) by misrepresenting to another tribunal that which led to its accomplishment.” Id. at 396. The district court found that “[t]his is what the Millers have done.” Id.
Based upon its findings of misconduct by the Millers and the usurpation of its exclusive jurisdiction to resolve interpretative questions under the MDL Settlement Agreement, the district court expressly invoked the All Writs Act, 28 U.S.C. § 1651(a), to enter the Injunction. According to the district court, such invocation was necessary “to protect the integrity of [its] processes and prevent the Honda MDL proceedings from being used for an improper purpose.... ” Id. at 396.
This timely appeal by the Millers followed in which the Millers challenge the Injunction on the ground that the district court lacked the authority to enter it. Also, Silver has filed a cross-appeal on the ground that the district court erred by [437]*437declining to adjudicate the merits of his lien on the Millers’ portion of the settlement funds.
II.
The overarching question presented in this appeal is whether the All Writs Act, 28 U.S.C. § 1651(a), gives a federal district court authority to enjoin judicial enforcement of an arbitration award, issued pursuant to state arbitration procedures, when: (1) the underlying arbitration resolved an issue over which the district court retained exclusive jurisdiction to resolve pursuant to an order by that district court approving a settlement agreement in MDL proceedings over which the district court possessed subject matter jurisdiction; and (2) the parties enjoined engaged in misconduct before the district court and the arbitrator in connection with the subject of the injunction.5 We begin our resolution of this question by setting forth the actual language of the All Writs Act and the established jurisprudence surrounding it.
The All Writs Act, 28 U.S.C. § 1651(a), provides that “[t]he Supreme Court and all courts established by Act of Congress may issue all writs necessary or appropriate in aid of their respective jurisdictions and agreeable to the usages and principles of law.” Id. Although the All Writs Act does not independently confer subject-matter jurisdiction on federal courts, Syngenta Crop Protection, Inc. v. Henson, — U.S. -, -, 123 S.Ct. 366, 370, 154 L.Ed.2d 368 (2002), it does “authorize a federal court ‘to issue such commands ... as may be necessary or appropriate to effectuate and prevent the frustration of orders it has previously issued in its exercise of jurisdiction otherwise obtained,’ ” Pennsylvania Bureau of Corr. v. United States Marshals Serv., 474 U.S. 34, 40, 106 S.Ct. 355, 88 L.Ed.2d 189 (1985) (quoting United States v. New York Tel. Co., 434 U.S. 159, 172, 98 S.Ct. 364, 54 L.Ed.2d 376 (1977)). Such authorization, however, does not control “[w]here a statute specifically addresses the particular issue at hand....” Pennsylvania Bureau of Corr., 474 U.S. at 43, 106 S.Ct. 355. For example, a party “may not, by resorting to the All Writs Act, avoid complying with the statutory requirements for removal” of a case in state court to federal court. Syngenta Crop Protection, Inc., — U.S. at -, 123 S.Ct. at 370.
Here, the district court enjoined the Millers from enforcing that portion of the arbitration award relating to their so-called “blue sky damages” in large measure to protect its exclusive jurisdiction to resolve interpretive questions under the MDL Settlement Agreement. The district court was also moved to action by its desire to rectify the injustice the district court found the Millers had perpetrated by engaging in misconduct in order to defeat such jurisdiction. We find no abuse of discretion in this regard.6
The district court’s possession of subject matter jurisdiction over the claims of the [438]*438Plaintiffs’ Class in the MDL Proceedings is not in dispute.7 Neither is it disputed that, pursuant to the district court’s Settlement Approval Order, the district court retained exclusive jurisdiction to interpret the terms of the MDL Settlement Agreement should any dispute over its meaning arise. The record in this case leaves no doubt that one of the key issues before the arbitrator was whether the MDL Settlement Agreement compensated the Millers for the inflated portion of the purchase price of their dealership attributable to the misallocation of Honda automobiles prior to their purchase of such dealership. Indeed, in order to establish the damages element of their legal malpractice claim against Silver, the Millers had to prove that but for Silver’s malpractice, they would have recovered the inflated portion of the purchase price of their dealership attributable to the misallocation of Honda automobiles prior to their purchase of such dealership. Coscia v. McKenna & Cuneo, 25 Cal.4th 1194, 108 Cal.Rptr.2d 471, 25 P.3d 670, 672 (Ca.2001) (“In a legal malpractice action arising from a civil proceeding, the elements are (1) the duty of the attorney to use such skill, prudence, and diligence as members of his or her profession commonly possess and exercise; (2) a breach of that duty; (3) a proximate causal connection between the breach and the resulting injury; and (4) actual loss or damage resulting from the attorney’s negligence.”).
Whether the Millers had already received full or partial compensation for the inflated portion of the purchase price of their dealership attributable to the misallo-cation of Honda automobiles prior to their purchase of such dealership undeniably raised an interpretive question under the MDL Settlement Agreement. Specifically, the Millers’ argument regarding “blue sky damages” versus “allocation damages” raised an interpretive question regarding what damages the Millers received for their “allocation claims” under the MDL Settlement Agreement. However, in flagrant disregard of the district court’s exclusive jurisdiction to resolve such interpretative question, the Millers argued before the arbitrator that they were not compensated under the MDL Settlement Agreement for what they termed “blue sky damages.” Accordingly, under all of the facts and circumstances that we have just outlined, we have no hesitancy in concluding that the Injunction was necessary to prevent direct frustration of the district court’s Settlement Approval Order, for which the district court undeniably possessed subject matter jurisdiction to issue.8 [439]*439We also have no trouble in concluding that the Injunction was necessary to cure the injustices created by the Millers through their abuse of the MDL process.
The Millers argue that, assuming ar-guendo the validity of these conclusions, the district court still abused its discretion in entering the Injunction because the Injunction did not meet any of the statutory requirements of the Anti-Injunction Act, 28 U.S.C. § 2283. Syngenta Crop Protection, Inc., — U.S. at -, 123 S.Ct. at 370 (a party may not, by resorting to the All Writs Act, avoid compliance with the requirements of a statute that specifically addresses the particular issue at hand).
The Anti-Injunction Act prohibits a federal court from enjoining “proceedings” in a state court “except as expressly authorized by Act of Congress, or where necessary in aid of its jurisdiction, or to protect or effectuate its judgments.” 28 U.S.C. § 2283. This prohibition extends to indirect injunctions against parties. Atlantic Coast Line R.R. Co. v. Brotherhood of Locomotive Eng’rs, 398 U.S. 281, 287, 90 S.Ct. 1739, 26 L.Ed.2d 234 (1970) (“It is well settled that the prohibition of § 2283 cannot be evaded by addressing the order to the parties or prohibiting utilization of the results of a completed state proceeding.”). For purposes of the Anti-Injunction Act, the term “proceedings” includes “all steps taken or which may be taken in the state court or by its officers from the institution to the close of the final process.” Hill v. Martin, 296 U.S. 393, 403, 56 S.Ct. 278, 80 L.Ed. 293 (1935).
For over two-hundred years, the Anti-Injunction Act “has helped to define our nation’s system of federalism.” Employers Res. Mgmt. Co., Inc. v. Shannon, 65 F.3d 1126, 1130 (4th Cir.1995). The three exceptions to the Anti-Injunction Act’s prohibition against enjoining state court proceedings “are construed narrowly, ... and are not [to] be enlarged by loose statutory construction.” Id. (internal quotation marks omitted) (alteration in original). The “necessary in aid of its jurisdiction” exception to the Anti-Injunction Act is widely understood to apply most often when a federal court was the first in obtaining jurisdiction over a res in an in rem action and the same federal court seeks to enjoin suits in state courts involving the same res. In re: Prudential Ins. Co. of Am. Sales Practice Litig., 261 F.3d 355, 365 (3d Cir.2001); 17 Charles Alan Wright, Arthur R. Miller, and Edward H. Cooper, Federal Practice and Procedure 2d, § 4225 (2d ed.1988). However, support for a broader application of the “necessary in aid of its jurisdiction” exception can be found in the Supreme Court’s statement that both this exception and the third exception to the Anti-Injunction Act allow federal injunctive relief against state court proceedings where it' is “necessary to prevent a state court from so interfering with a federal court’s consideration or disposition of a case as to seriously impair the federal court’s flexibility and authority to decide that case.” Atlantic Coast Line R.R. Co., 398 U.S. at 295, 90 S.Ct. 1739. And as some legal scholars have pointed out, “[t]here have been some signs of such flexibility in the recent cases.” Federal Practice and Procedure 2d § 4225 at 531.
The most prominent area of such flexibility is school desegregation cases. “In the school desegregation area the federal court typically takes a controversy in hand, modifying its orders as need be from time to time, and it has been held that the court can enjoin state proceedings that would interfere with the federal court’s continuing jurisdiction.” Id. Indeed, in a school desegregation case, we have relied upon the “necessary in aid of its jurisdiction” exception to the Anti-Injunction Act in upholding an injunction restraining a state [440]*440court suit: (1) in which the plaintiffs claimed that the school board was discriminating against white children with respect to the statutory standards applicable to exceptionally talented children; and (2) where plaintiffs’ claims could not be separated from the order previously entered by the district court. Swann v. Charlotte-Mecklenburg Bd. of Educ., 501 F.2d 383 (4th Cir.1974). Especially relevant to the appeal before us is the fact that, in the multi-district litigation area, some courts have permitted injunctions against parallel state court proceedings under the “necessary in aid of its jurisdiction” exception where such state court proceedings threatened to frustrate multi-district litigation proceedings and disrupt the orderly resolution of those proceedings. In re: Prudential Ins. Co. of Am. Sales Practice Litig., 261 F.3d at 365 (collecting cases); Winkler v. Eli Lilly & Co., 101 F.3d 1196, 1202 (7th Cir.1996) (collecting cases) (“We agree that the necessary in aid of jurisdiction exception [to the Anti-Injunction Act] should be construed to empower the federal court to enjoin a concurrent state proceeding that might render the exercise of the federal court’s jurisdiction nugatory.” (internal quotation marks omitted)).
The “to protect or effectuate its judgments,” language of the Anti-Injunction Act has come to be known as “the relitigation exception” to the Anti-Injunction Act. According to the Supreme Court, “[t]he relitigation exception was designed to permit a federal court to prevent state litigation of an issue that previously was presented to and decided by the federal court. It is founded in the well-recognized concepts of res judicata and collateral estoppel.” Chick Kam Choo v. Exxon Corp., 486 U.S. 140, 147, 108 S.Ct. 1684, 100 L.Ed.2d 127 (1988). An injunction may issue under the relitigation exception only if the claims or issues subject to the injunction have actually been decided. Id. at 148, 108 S.Ct. 1684 (stating that the court must look to what the previous order “actually said” and may not “render a post hoc judgment as to what the order was intended to say”); LCS Servs., Inc. v. Hamrick, 925 F.2d 745, 749 (4th Cir.1991) (“a complainant seeking to avail himself of the relitigation exception to the [Anti-Injunction] statute must make a strong and unequivocal showing of relitigation of the same issues”) (internal quotation marks omitted).
Because the Millers failed to argue below that the Injunction did not fall within one of the express exceptions to the Anti-Injunction Act, we are constrained to review any alleged error on the part of the district court with respect to the Anti-Injunction Act under the plain error standard of review. In re: Celotex Corp., 124 F.3d 619, 630-31 (4th Cir.1997) (adopting plain error standard of review used in criminal cases, as set forth in United States v. Olano, 507 U.S. 725, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993), for application in civil cases). Under the plain error standard of review, we may only exercise our discretion to correct a forfeited error, if we: (1) find error; (2) find the error is plain; (3) find the error affects the substantial rights of the party or parties alleging the error; and (4) after examining the particulars of the case, we find the error seriously affects the fairness, integrity or public reputation of judicial proceedings. Id. at 630-31.
Our application of the plain error test to the alleged error by the district court reveals that the Millers are not entitled to vacature of the Injunction on the basis of the Anti-Injunction Act. Assuming arguendo that the first element of the plain error test is met, i.e., the Injunction violates the Anti-Injunction Act because it enjoins a state court proceeding and each of the Act’s three exceptions are inapplicable, the second element of the plain error [441]*441test is not met, i.e., the error is not plain. For purposes of the plain error test, the term “ ‘[p]lain’ is synonymous with ‘clear’ or, equivalently,’obvious,’ ” Olano 507 U.S. at 734, 113 S.Ct. 1770, under the law at the time of our appellate consideration, Johnson v. United States, 520 U.S. 461, 468, 117 S.Ct. 1544, 137 L.Ed.2d 718 (1997). At the present time, the law is not clear or equivalently obvious that the “necessary in aid of jurisdiction” exception to the Anti-Injunction Act’s general prohibition against a federal court enjoining a state court proceeding is inapplicable to the, Injunction. First, we have already concluded under our discussion of the All Writs Act that the Injunction was necessary to vindicate the district court’s exclusive jurisdiction to resolve interpretive questions under the MDL Settlement Agreement. Thus, the plain text of the “necessary in aid of jurisdiction” exception is applicable. Second, as we have already set forth, some federal appellate courts have permitted injunctions under the same exception where a parallel state court action threatens to frustrate federal multi-district litigation proceedings and disrupt the orderly resolution of those proceedings. E.g., Carlough v. Amchem Products, Inc., 10 F.3d 189, 202-03 (3d Cir.1993) (holding that it was appropriate as necessary in aid of the district court’s jurisdiction in class action asbestos suit to enjoin absent members of plaintiff class from seeking a ruling from state court permitting mass opting out of all plaintiffs in that state, at mature phase of federal settlement proceedings and after years of pretrial negotiation). Here, a strong argument can be made that enforcement of the arbitration award in favor of the Millers threatens to frustróte the district court’s ability to provide a universal interpretation of the term “allocation claim” under the MDL Settlement Agreement, which interpretive question may also arise in the future pursuant to litigátion involving other parties to the MDL.- In sum, assuming the existence of error, the error is not plain.
Moreover, assuming arguendo that the first three elements of the plain error test are satisfied, several factors' strongly 'weigh against our finding that the assumed error seriously affects the fairness, integrity or public reputation of judicial proceedings and will continue to do so unless the assumed error is corrected. First, the Millers do not claim that they in any way lacked the opportunity to raise the Anti-Injunction Act below as a defense to the Injunction. Second, the Millers, as found by the district court and supported by the record on appeal, intentionally mislead the district court at a critical motion stage into believing that they did not intend to make any arguments before the arbitrator that would raise, interpretive questions under the MDL Settlement Agreement. Third, despite the Millers’ knowledge that the district court retained exclusive jurisdiction to resolve interpretive questions under the MDL Settlement Agreement, the Millers intentionally made arguments before the arbitrator that they knew necessarily raised interpretive questions under the MDL Settlement Agreement. Fourth and finally, as determined by the district court, the Millers were already compensated, under the MDL Settlement Agreement, for their so-called “blue sky damages.” In sum, we cannot conclude that the facts here call for us to exercise our discretion to correct an assumed error not raised below.9
III.
As we previously stated, under all of-the facts and circumstances of this case,’ we [442]*442have no difficulty in concluding that the Injunction was necessary to prevent direct frustration of the district court’s Settlement Approval Order and to cure injustice created by the Millers through their abuse of the MDL process. Accordingly, we find no abuse of discretion with respect to the district court’s invocation of the All Writs Act to enjoin the Millers from enforcing the “blue sky damages” portion (including related attorneys’ fees) of their multi-mil-lion dollar arbitration award. Therefore, we_ affirm the district court’s order entering the Injunction.10
AFFIRMED.