The Shaw Group ("Shaw") sued Dorsey McCall, its former employee, in state court for allegedly violating noncompete and nonsolicitation agreements. After being acquired in part by Aptim Corporation ("Aptim"), Shaw sought to dismiss its state action while Aptim pursued a federal-court action to enforce the arbitration clause in McCall's employment contract. The federal district court declined to abstain, it compelled arbitration, and it stayed the state-court proceeding. We find no error and affirm.

I.

McCall resigned from Shaw in January 2016. He then began working for an affiliate of Bernhard Capital Partners Management LP and later became the CEO of Allied Power Management, LLC ("Allied"), a direct competitor of Shaw's. Believing that McCall had violated the noncompete and nonsolicitation agreements in his employment contract, Shaw sued McCall in state court. 1 Those agreements state that arbitration will occur in New Orleans and that the employer may file for injunctive relief from a judicial authority without waiving the right to arbitrate the underlying dispute.

On June 15, 2017, Shaw sued in state court, requesting injunctive relief and damages. The state court issued a Joint Protective Order. 2 On June 30, Aptim acquired Shaw's capital services segment, which included the rights to McCall's employment agreement. Aptim and Shaw moved to substitute Aptim in the state-court *135 action on July 6, which McCall opposed on July 10. On July 17, Aptim and Shaw withdrew their motion for substitution. That same day, Aptim filed a demand for arbitration with the American Arbitration Association, and Shaw filed both an amended petition, deleting its request for damages, and a motion to dismiss the amended petition with prejudice. McCall filed an opposition to the motion for voluntary dismissal, an answer to Shaw's complaint, a reconventional demand, a petition for declaratory judgment, a motion to consolidate, and a motion for constructive contempt against Aptim for demanding arbitration in violation of the protective order, though Aptim was not then a party to the case.

On August 21, Aptim, without Shaw, sued in federal court to compel arbitration and to stay the state-court proceeding, seeking arbitration on the same contractual violations that Shaw had raised in state court: that McCall had breached his noncompete agreement by working for Allied and his nonsolicitation agreement by poaching fifteen of Shaw's senior employees. Before the federal court ruled, the state court on September 1 issued an order joining Aptim in the state-court action effective June 30 (the day the motion for substitution had been originally filed); finding that Aptim and Shaw had waived their arbitration rights by initiating the state-court action; and granting McCall's motion to stay arbitration.

On September 19, the federal district court ordered Aptim and McCall to arbitrate their dispute and stayed the state-court action as between Aptim and McCall. On September 25, the court clarified its order to state that all persons and entities in privity with Aptim and McCall must submit to arbitration, thus staying the state-court litigation by McCall against Shaw. On appeal, McCall asserts the federal district court erred by declining to abstain under Colorado River Water Conservation District v. United States , 424 U.S. 800 , 817, 96 S.Ct. 1236 , 47 L.Ed.2d 483 (1976), erred by compelling the parties to arbitrate, and violated the Anti-Injunction Act by enjoining the state-court proceedings.

II.

A Colorado River abstention analysis begins with a heavy thumb on the scale in favor of exercising federal jurisdiction, and that presumption is overcome only by "exceptional circumstances." Stewart v. W. Heritage Ins. Co. , 438 F.3d 488 , 491 (5th Cir. 2006). Federal courts have a "virtually unflagging obligation ... to exercise the jurisdiction given them." Colo. River , 424 U.S. at 817 , 96 S.Ct. 1236 . Even so, a court may choose to abstain, awaiting the conclusion of state-court proceedings in a parallel case, based on principles of "[w]ise judicial administration, giving regard to conservation of judicial resources and comprehensive disposition of litigation." Id. (quoting Kerotest Mfg. Co. v. C-O-Two Fire Equip. Co. , 342 U.S. 180 , 183, 72 S.Ct. 219 , 96 L.Ed. 200 (1952) ).

Whether to abstain is not a question answered by the recitation of "a mechanical checklist" but instead rests "on a careful balancing of the important factors as they apply in a given case, with the balance heavily weighted in favor of the exercise of jurisdiction." Moses H. Cone Mem'l Hosp. v. Mercury Constr. Corp. , 460 U.S. 1 , 16, 103 S.Ct. 927 , 74 L.Ed.2d 765 (1983). To determine whether exceptional circumstances are present, the court considers the following six factors:

(1) assumption by either court of jurisdiction over a res, (2) relative inconvenience of the forums, (3) avoidance of piecemeal litigation, (4) the order in which jurisdiction was obtained by the *136 concurrent forums, (5) to what extent federal law provides the rules of decision on the merits, and (6) the adequacy of the state proceedings in protecting the rights of the party invoking federal jurisdiction.

Stewart , 438 F.3d at 491 . We review for abuse of discretion the district court's decision whether to abstain, and we exercise de novo review to the extent that the decision turns on an interpretation of law. Black Sea Inv., Ltd. v. United Heritage Corp. , 204 F.3d 647 , 649-50 (5th Cir. 2000).

McCall asserts that there are exceptional circumstances because the state court issued a ruling on the question of arbitrability before the federal court ruled. This case, however, is subject to the same discretionary balancing of the Colorado River factors as any other abstention inquiry.

A.

The first factor weighs against abstention. Because this is an in personam action, there is no res . An absence of property is not "a merely neutral item, of no weight in the scales." 3 Instead, it "supports exercising federal jurisdiction." 4

B.

The second factor is neutral. The relative convenience of the forums "primarily involves the physical proximity of the federal forum to the evidence and witnesses." Evanston , 844 F.2d at 1191. The question requires finding not that the state court is a "better" or "more convenient" forum but that the "inconvenience of the federal forum is so great" as to warrant abstention. Id. at 1192. "When courts are in the same geographic location, the inconvenience factor weighs against abstention." Stewart , 438 F.3d at 492 . The state courthouse is in Baton Rouge, and the federal district court is in New Orleans. Both Allied and Shaw are headquartered in Baton Rouge, and McCall resides closer to Baton Rouge than to New Orleans. The 80-mile distance does not compare to the 300-mile distance in Colorado River . 5 The two courthouses are within the *137 same geographic location for all practical purposes. Because nothing in this case demonstrates that the inconvenience of the federal forum is "so great," Evanston , 844 F.2d at 1191, this factor is neutral at best.

C.

The third factor weighs against abstention. Given the strong federal policy favoring arbitration, the concern about piecemeal litigation "is not applicable in the FAA context." Safety Nat'l Cas. Corp. v. Bristol-Myers Squibb Co. , 214 F.3d 562 , 565 (5th Cir. 2000). Piecemeal litigation is a different concern from the worry of obtaining conflicting judgments in parallel actions involving the same parties and the same questions. The remedy for conflicting judgments is not abstention, but the application of res judicata . Kelly Inv., Inc. v. Cont'l Common Corp. , 315 F.3d 494 , 498 (5th Cir. 2002).

D.

The fourth factor, regarding the order in which jurisdiction was obtained, slightly favors abstention. The inquiry centers more on the progress made in the relative forums, not on the date of initial filing. Moses H. Cone , 460 U.S. at 21 , 103 S.Ct. 927 . If the progress made is just "jurisdictional posturing" with little progress on the merits, the factor "weighs against abstention." Black Sea Inv. , 204 F.3d at 651 . This factor is difficult to weigh, as the parties characterize the timeline and progress quite differently. And it is unusual in our abstention jurisprudence to confront a case in which the same side filed both the state and federal actions, though Aptim was not a party to the state suit when it filed in federal court.

Numerous motions were filed in state court before the federal case began. The state and federal action were filed on June 15 and August 21, respectively. Aptim was not joined in the state action until September 1, which was more than a week after it filed its federal action and was several weeks after it and Shaw had withdrawn the motion to substitute and Shaw had attempted to dismiss the suit entirely on July 17.

Despite the number of filings, the state action was not necessarily progressing. When the federal suit was filed at the end of August, the state court had not ruled on any of Shaw's July 17 motions, none of which concerned the merits. Shaw sought to dismiss before any rulings had been issued and only one month after filing. In fact, Shaw even sought and was granted mandamus from the state appellate court ordering the state trial court to rule on Shaw's motion to dismiss voluntarily by August 23. The state court denied the voluntary dismissal on August 24. It was not until September 1 that the state court made any progress.

Before the federal court compelled arbitration, the state court issued an order staying the arbitration Aptim had initiated. Thus, this factor favors arbitration, but only slightly, considering the complete set of circumstances. Aptim sought arbitration just weeks after acquiring Shaw, the state court had made minimal progress when the district court action was filed, and Aptim was a nonparty in the state-court proceeding until the state court simultaneously issued the stay and joined it in the suit.

McCall insists that the fact that the state trial court ruled on whether arbitration should proceed, and did so before the federal district court did, should be accorded almost decisive weight. McCall would be correct if the state trial court's ruling would be res judicata or would collaterally estop Aptim. If a state court's ruling would be given preclusive effect by *138 another court of that state, then federal courts must also give preclusive effect to that ruling. 6 If the preclusive ruling is dispositive of the federal action, then the federal court should abstain and dismiss because there is no point in proceeding further, irrespective of the other relevant factors in assessing abstention under Colorado River . 7

McCall does not contend that the state court's determination that Shaw and Aptim waived their rights to arbitrate would be given preclusive effect by Louisiana courts. In fact, at the hearing, the federal district court stated "that there was no final judgment, so neither res judicata nor issue preclusion applies." 8 McCall did not take issue with that statement and does not contend that preclusion applies. To the contrary, in his briefing in our court, McCall opines that the federal district court's stay of the state court proceedings "ensur[es] that the state court would never be able to enter a final judgment entitled to preclusive effect." Accordingly, the state court's ruling is not decisive regarding abstention because the state court's interlocutory ruling regarding arbitration is not entitled to full faith and credit under the Full Faith and Credit Act. 9

Greater progress alone "does not give rise to 'exceptional circumstances' capable of overcoming the strong presumption in favor of retaining jurisdiction." Saucier , 701 F.3d at 465. Instead, the federal and state courts have concurrent jurisdiction, and the state court was not so far ahead as to counsel the federal court to stay its hand. Just as we concluded under the third factor, the solution to inconsistent judgments is through a plea of res judicata after one court enters a final judgment.

E.

The fifth factor weighs against abstention. "The presence of a federal law issue 'must always be a major consideration weighing against surrender [of jurisdiction],' but the presence of state law issues weighs in favor of surrender only in rare circumstances." Murphy v. Uncle Ben's, Inc. , 168 F.3d 734 , 739 (5th Cir. 1999) (quoting Evanston, 844 F.2d at 1193 ).

The Federal Arbitration Act ("FAA") is the underlying law and embodies "a liberal federal policy favoring arbitration agreements," Moses H. Cone , 460 U.S. at 24 , 103 S.Ct. 927 , that serves as the backdrop for any FAA litigation. The FAA

*139 itself is an outlier: It created substantive federal law but not federal-question jurisdiction. Thus its enforceability is left largely to state courts. Id. at 25 n.32, 103 S.Ct. 927 ("[A]lthough enforcement of the [FAA] is left in large part to the state courts, it nevertheless represents federal policy to be vindicated by the federal courts where otherwise appropriate."). This factor, therefore, has less significance but still weighs against abstention. Id. at 25-26 , 103 S.Ct. 927 .

F.

The sixth factor, evaluating the adequacy of state proceedings to protect the rights of the party invoking federal jurisdiction, can only be neutral or weigh against abstention. Stewart , 438 F.3d at 493 . Nothing has impugned the state court's ability fairly to determine the legal questions at issue, so this factor is neutral.

G.

Reviewing the six factors, two are neutral, one weighs slightly in favor of abstention, and three weigh against abstention. To overcome the strong presumption in favor of federal jurisdiction, a party must show exceptional circumstances. The factors here do not demonstrate such circumstances, and the district court was correct to exercise jurisdiction.

H.

McCall points to three out-of-circuit decisions in which the state court ruled first and the appellate court found abstention proper. He contends those cases demonstrate that the state court's issuance of a ruling should be a primary focus of the abstention inquiry, almost to the point of being conclusive. In addition to our treatment of this contention under the fourth factor, we address each of these cases in turn.

1.

In Vulcan Chemical Technologies, Inc. v. Barker , 297 F.3d 332 (4th Cir. 2002), suit was filed in the state court, which compelled arbitration. Arbitration concluded with a multi-million dollar judgment on the merits against Vulcan, which sued in federal court to vacate the award. The state court confirmed the award before the federal court ruled. Id. at 335 . After the federal district court had vacated the award two months after the state court's confirmation of it, the Fourth Circuit reversed, finding that five of the six Colorado River factors favored abstention and one was neutral. Id. at 341-43 .

In addition to undertaking the typical six-factor analysis, the Fourth Circuit noted that the motive for filing in federal court was critical. Up until the arbitrator entered its award, Vulcan had "gladly litigated" in state court and had "gladly arbitrated there before an agreed-upon arbitrator." Id. at 343 . Its federal filing was merely a "strategy to obtain a second opinion." Id.

The same is not true here. In Vulcan , over two years of litigation and a complete disposition of the merits had occurred in state court before the federal filing. Aptim filed in federal court before the state court had done anything on the merits, so its motive could not have been to get a second opinion. Instead, Aptim asserted its arbitration rights on July 17, just weeks after acquiring Shaw.

2.

McCall points next to Preferred Care of Delaware, Inc. v. VanArsdale , 676 Fed.Appx. 388 (6th Cir. 2017). Based on the particular facts of the case and the state-law *140 issue underlying the state-court decision on arbitrability, the Sixth Circuit affirmed the abstention. The opinion divided Colorado River 's six-factor test into eight factors and found that the first two weighed slightly against abstention, five strongly favored abstention, and one was neutral. Id. at 394-97 .

This is again far different from how the factors play out in the present case. The Sixth Circuit examined each factor in turn and did not base its ruling solely on the fact that the state court issued an order finding the arbitration clause invalid under state law before the federal court ruled. No state-law question is at issue here, and the weighing of the factors is inherently discretionary and cannot turn on the presence or absence of one fact.

3.

Finally, D.A. Osguthorpe Family Partnership v. ASC Utah , Inc. , 705 F.3d 1223 (10th Cir. 2013), is readily distinguished. The state suit began in 2006. Numerous issues and parties were involved in a complex proceeding. "[T]he [state court] litigation has not so much developed as it has metastasized: parties have proliferated, claims have collided, and issues have become intimately entangled." Id. at 1226 . After five years and the issuance of multiple decisions that went all the way to the state supreme court, one of the losing parties filed in federal court to compel arbitration. Id. at 1227-29 .

The Tenth Circuit affirmed the decision to abstain. It found four of the factors were neutral and two-the third and fourth-weighed heavily in favor of abstention. Id. at 1234-35 . In examining the progress made in the state court, the court of appeals found that the "realities of the case at hand" must guide a court's factorial analysis. Id. at 1236 (quoting Moses H. Cone , 460 U.S. at 21 , 103 S.Ct. 927 ). That years, not weeks, had passed in state court without objection, that the case was "interwoven" with the "trial and appellate levels" of the state-court system, and that "vexatious or reactive" motives were at play, were heavy considerations favoring abstention. Id. at 1235.

Conversely, in the present suit, weeks, not years, had passed in state court when the federal action was filed, and no vexatious motivation is discernible given the timeline of events. There is no comparison between the expansive litigation at issue in D.A. Osguthorpe and the mere months in the case at hand.

Colorado River presents an inherently discretionary balancing inquiry that shifts with the particular facts. Given our facts, the district court did not abuse its discretion in declining to abstain.

III.

Having found that the district court did not abuse its discretion in declining to abstain, we turn to its finding that Aptim did not waive its arbitration rights. This court reviews the issue of waiver de novo . Walker v. J.C. Bradford & Co. , 938 F.2d 575 , 577 (5th Cir. 1991).

The right to arbitrate can be waived if a party "(1) 'substantially invokes the judicial process' and (2) thereby causes 'detriment or prejudice' to the other party." 10 Given the strong federal policy in favor of arbitration, the party seeking to prove waiver must overcome the heavy presumption against such a finding. 11

*141 There is not enough here to overcome that presumption.

A.

Shaw's initial complaint raising a claim for damages is enough for substantial invocation under Nicholas v. KBR, Inc. , 565 F.3d 904 , 908 (5th Cir. 2009). In Nicholas , the court found that "filing suit without asserting an arbitration clause constitutes substantial invocation of the judicial process." Id.

The purpose of the Nicholas rule is to divine a plaintiff's intent regarding its choice of forum for litigating the merits of an arbitrable claim. Though a defendant may allow significant time to pass and may engage in some preliminaries of litigation without the court's finding substantial invocation, 12 a plaintiff's "disinclination to resort to arbitration" can be seen at the filing stage. Id. (quoting Miller , 781 F.2d at 497 ). The court laid out two exceptions to this assumption: filing suit to determine the presence of an enforceable arbitration agreement and filing to obtain injunctive relief pending arbitration. Id.

The facts of the present case, however, defy easy application of this seemingly straightforward rule. In Nicholas , the filing of a lawsuit on the merits was followed by actual merits litigation, and the court found especially troubling the plaintiff's decision to seek arbitration following an adverse ruling. Id. at 909. The present appeal does not implicate the feared second bite at the apple. Further, it is complicated by Aptim's delayed entrance into the litigation and McCall's contradictory postures in state and federal court regarding Aptim's status.

Shaw had the contractual right to seek injunctive relief in court without compromising its arbitration rights. Its initial filing, including a claim for damages, however, is enough under Nicholas to find substantial invocation of the judicial process, though still leaving open the question of prejudice to McCall. The dispute then arises whether Shaw's conduct in filing the initial complaint is imputed to Aptim.

In contending that Shaw's conduct should be attributable to Aptim, McCall tries to have his cake and eat it too. In state court, McCall opposed Aptim and Shaw's motion for substitution, stating that it was unclear which rights Shaw assigned to Aptim and whether Aptim was a successor such that substitution was proper. Then, in its federal filings, McCall treated Aptim and Shaw as one and the same party, using the very language of the motion it opposed to assert that Aptim stepped into the shoes of Shaw and thus inherited Shaw's substantial invocation of the judicial process.

The state court never ruled on the motion or the opposition before Aptim and Shaw withdrew the motion. The court later joined Aptim as a party and bound it to all prior rulings but neither substituted Aptim nor dismissed Shaw, making no apparent judgment about Aptim's status as a successor under the assignment agreement. The federal district court was rightly concerned about the appearance that McCall tried to keep Aptim out of the litigation but then sought to have Aptim bound by rulings made while it was actively denied the ability to defend itself.

*142 Absent imputation, Aptim did not substantially invoke the judicial process. It did not file anything regarding the merits or ask for damages but filed only a motion for substitution and a motion withdrawing the request for substitution. A nonparty to the suit, Aptim demanded arbitration only one month after the state-court litigation had begun and only eleven days after it had sought unsuccessfully to be substituted into the action. If Shaw's filing the initial complaint is not imputed to Aptim, Aptim's actions alone are inadequate for substantial invocation. This inquiry is simplified by the absence of prejudice, thus obviating the need to interpret the assignment agreement and determine imputation.

B.

To support a finding of waiver, McCall must demonstrate prejudice. "Prejudice in the context of arbitration waiver refers to delay, expense, and damage to a party's legal position." Nicholas , 565 F.3d at 910 . Courts considering prejudice look to things such as how much discovery has been conducted and how much the litigation relates to the merits. 13 Minimal discovery does not demonstrate prejudice. Tenneco Resins , 770 F.2d at 421.

McCall does not show prejudice. Before Aptim's acquisition of Shaw, the state court held a hearing on the TRO, and Shaw, McCall, and Allied entered into a protective order. All of those proceedings relate to the injunctive relief that Shaw was contractually permitted to seek without compromising its arbitration rights. Additionally, Shaw dropped the damages claim only one month after filing, with no proceedings that would have cost McCall time, money, or strategic advantage. The case was ongoing for just over two months before the federal filing and for only one month before the initial arbitration demand. During that time, around June 30 when Aptim acquired part of Shaw, discovery was stayed for the parties to sort out the consequences of the acquisition, and the preliminary-injunction hearing was cancelled. McCall cannot demonstrate the time, expense, or disadvantage in litigating position required to show prejudice.

IV.

We must now determine whether the federal district court erred in enjoining the state-court proceedings under the relitigation exception to the Anti-Injunction Act. Because, under the Act, a federal court is entitled to defend its own final judgment, we uphold the injunction. 14

The Anti-Injunction Act states, "A court of the United States may not grant an injunction to stay 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 . The prohibition against interfering in state proceedings embodies a strong policy that, recognizing the "independence of the States and their courts, the exceptions should not be enlarged."

*143 Atl. Coast Line R.R. Co. v. Bhd. of Locomotive Eng'rs , 398 U.S. 281 , 287, 90 S.Ct. 1739 , 26 L.Ed.2d 234 (1970). A federal court cannot enjoin a state-court suit on the grounds that "the state court may have taken action which the federal court [is] certain [is] improper," nor is it appropriate to avoid simultaneous pursuit of claims in courts with concurrent jurisdiction. Id. at 295-96 , 90 S.Ct. 1739 .

Under the Act, an injunction is not appropriate just because it is "related" to the federal court's jurisdiction. Id. at 295 , 90 S.Ct. 1739 . If the state court takes an action the federal court or a party to the action finds incorrect, the proper course is typically the state appellate court. Id. at 296 , 90 S.Ct. 1739 . Any doubts about the "propriety of a federal injunction ... should be resolved in favor of permitting the state courts to proceed.... The explicit wording of § 2283 itself implies as much." Id. at 297 , 90 S.Ct. 1739 .

The federal district court invoked the relitigation exception, stating that the injunction was necessary to "protect or effectuate its judgment[ ]." This 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." Chick Kam Choo v. Exxon Corp. , 486 U.S. 140 , 147, 108 S.Ct. 1684 , 100 L.Ed.2d 127 (1988). McCall asserts that the Act prevents a federal court from enjoining an already issued state court ruling.

The application of the Act is not so temporally bound. Instead, the inquiry turns on the question of finality. A federal court that has entered a final judgment entitled to preclusive effect may, "to protect or effectuate its judgment[ ]," stay state-court proceedings when it is clear that the state court ruling that would interfere with the enforcement of the federal court's judgment is not preclusive and is not entitled to full faith and credit.

For example, in Atlantic Coast Line , a federal court in 1967 refused to enjoin the BLE union from picketing at a railroad switching yard. The railroad then promptly obtained an injunction in state court that prohibited the picketing. Two years later, the Supreme Court reviewed a state-court injunction against picketing by the BLE and other unions in a nearby area and held that the unions had a federally protected right to picket. Atl. Coast Line , 398 U.S. at 283-84 , 90 S.Ct. 1739 (citing Bhd. of R.R. Trainmen v. Jacksonville Terminal Co. , 394 U.S. 369 , 89 S.Ct. 1109 , 22 L.Ed.2d 344 (1969) ). The BLE then returned to state court seeking dissolution of the 1967 injunction, but "the state judge refused to dissolve the injunction, holding that [the Supreme Court's] Jacksonville Terminal decision was not controlling." Id. at 284, 90 S.Ct. 1739 . The union did not appeal that decision but instead requested the federal court to issue an injunction against the enforcement of the 1967 state-court injunction. The federal court did so, and the Supreme Court reversed.

Were the timeline the sole deciding factor, the Court could have based its decision on the fact that the state injunction preceded the federal litigation. Instead, the Court found that the language "necessary in aid" of a federal court's jurisdiction in the Anti-Injunction Act "implies something similar to the concept of injunctions to 'protect or effectuate' judgments." Id. at 295 , 90 S.Ct. 1739 . There was no federal-court judgment that needed to be defended against state litigation. Instead, the federal-court litigation involved claims under federal law, and the state-court litigation involved claims based on state law and the union's defense regarding the preclusive effect of federal law. Id. "In short, the state and federal courts had concurrent jurisdiction in this case, and neither court was free to prevent either party from simultaneously *144 pursuing claims in both courts." Id. "The state court's assumption of jurisdiction over state law claims and the federal preclusion issue did not hinder the federal court's jurisdiction so as to make an injunction necessary to aid that jurisdiction." Id. at 296 , 90 S.Ct. 1739 .

The Court used the same language of preclusion in Parsons Steel . Though the state-court ruling did not precede the federal court's final judgment, the Court's reasoning, which focused on the Full Faith and Credit Act, applies regardless of the order of the state and federal decisions.

In Parsons Steel , a bank obtained a final judgment in its favor in federal district court that was affirmed on appeal. Parallel proceedings had been ongoing in state court, which rejected the bank's argument that the federal judgment was res judicata . The state-court case proceeded to trial, and a jury returned a verdict adverse to the bank. Id. The bank then returned to federal district court and obtained an injunction prohibiting plaintiffs from proceeding further in the state action. Parsons Steel , 474 U.S. at 520-21, 106 S.Ct. 768 .

In the succeeding challenge to the federal injunction, the Supreme Court first recognized that "under the Full Faith and Credit Act a federal court must give the same preclusive effect to a state-court judgment as another court of that State would give." Id. at 523, 106 S.Ct. 768 . The Court held that the federal district court had erred by failing to "consider the possible preclusive effect under Alabama law of the state-court judgment, and particularly of the state court's resolution of the res judicata issue." Id. The federal district court had concluded that "the relitigation exception to the Anti-Injunction Act limits the Full Faith and Credit Act." Id. The Supreme Court disagreed: "We believe that the Anti-Injunction Act and the Full Faith and Credit Act can be construed consistently, simply by limiting the relitigation exception of the Anti-Injunction Act to those situations in which the state court has not yet ruled on the merits of the res judicata issue." Id. at 524, 106 S.Ct. 768 .

The Court once again confirmed that lower federal courts do not sit in review of state-court decisions and that "[c]hallenges to the correctness of a state court's determination as to the conclusive effect of a federal judgment must be pursued by way of appeal through the state-court system and certiorari from this Court." Id. at 525, 106 S.Ct. 768 . Even if the state court incorrectly resolved the res judicata claim, that would not justify a lower-federal-court injunction. Id.

Nevertheless, the federal district court was not foreclosed from enjoining state-court proceedings on other grounds if that court, upon considering the preclusive effect under state law, found that Alabama would not in fact consider the judgment preclusive. In that instance, the federal district court could then "decide the propriety of a federal-court injunction under the general principles of equity, comity, and federalism." Id. at 526, 106 S.Ct. 768 . This decision directs that in determining whether a stay of state-court proceedings was necessary under the Anti-Injunction Act, a federal district court's and this court's focus should be on the preclusive effect of a state-court ruling.

Chick Kam Choo further bolsters this conclusion, stating that the relitigation exception is "founded in the well-recognized concepts of res judicata and collateral estoppel." Chick Kam Choo , 486 U.S. at 147 , 108 S.Ct. 1684 . This does not permit a federal court to enjoin a state-court ruling out of disagreement. But when the federal court issues a final judgment, the relitigation exception employs the foundation laid *145 in the Full Faith and Credit Act and permits the federal court to enjoin proceedings contrary to that judgment.

Our circuit has applied this reasoning several times, stating that the relitigation exception "allows an injunction where state proceedings threaten to undermine a federal judgment having preclusive effect under the 'well-recognized concept' of collateral estoppel." 15 We do so again and determine that the injunction was proper to defend the federal district court's final judgment in the face of a non-preclusive state-court order.

V.

In sum, the federal district court did not abuse its discretion in declining to abstain, Aptim did not waive its arbitration rights, and the district court properly invoked the relitigation exception to defend its final judgment. Therefore, its judgment is AFFIRMED.

PRISCILLA R. OWEN, Circuit Judge, concurring and dissenting:

I agree with, and join, the court's thorough and thoughtful opinion, with the exception of footnote 14, and the court's affirmance of the district court's judgment in its entirety. I would reverse the district court's judgment to the extent that it purports to enjoin the state-court litigation as to The Shaw Group, Inc. (Shaw). I also write separately to address statements in Supreme Court opinions that, at least facially, lend support to McCall's contention that the federal district court was powerless under the Anti-Injunction Act to stay state-court proceedings because the state trial court ruled that arbitration had been waived before the federal district court addressed that issue and entered a final judgment. The state trial court's ruling, as McCall concedes, would not be given preclusive effect. Therefore, the state court's interlocutory ruling was not an impediment to the federal district court's ability to issue a stay to protect and effectuate its final judgment compelling arbitration between Aptim and McCall.

I

With regard to the Anti-Injunction Act, first and foremost, nothing in the text of the Act suggests that a federal district court must defer to a prior, interlocutory, non-preclusive state-court ruling in an ongoing state proceeding once the federal district court enters a final judgment concerning the same issue and parties. 1 Second, as the Supreme Court has recognized, the final phrase in the Anti-Injunction Act, that permits federal courts to stay state-court proceedings "to protect or effectuate its judgments," 2 "is founded in the well-recognized concepts of res judicata and collateral estoppel." 3 Well-recognized concepts of res judicata and collateral estoppel permit a final judgment to have preclusive effect when another court in concurrent or parallel proceedings has ruled to the contrary, if that *146 prior ruling was not a final judgment or was not entitled to preclusive effect. 4

The Supreme Court reviewed the history of the development of the Anti-Injunction Act in Atlantic Coast Line Railroad Co. v. Brotherhood of Locomotive Engineers . 5 Our country, it explained, has "two essentially separate legal systems," and "[e]ach system proceeds independently of the other with ultimate review in [the Supreme Court] of the federal questions raised in either system." 6 The Supreme Court explained that "[p]roceedings in state courts should normally be allowed to continue unimpaired by intervention of the lower federal courts, with relief from error, if any, through the state appellate courts and ultimately this Court." 7 But "this dual court system was bound to lead to conflicts and frictions," and "[t]he 1793 anti-injunction Act was at least in part a response to these pressures." 8 There are "three specifically defined exceptions" in the present-day Anti-Injunction Act to its otherwise "absolute prohibition against enjoining state court proceedings." 9 The Supreme Court has never held that to come within one of these exceptions, the federal court's final judgment must precede any state ruling on the issue resolved by the federal court's judgment.

In Chick Kam Choo v. Exxon Corp. , the Supreme Court described the final phrase in the Anti-Injunction Act, "to protect or effectuate its judgments," 10 as a "relitigation exception" that "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." 11 The word "previously" cannot bear the weight that McCall, in the present case, places upon it. It is only after an issue has been presented to and decided by a federal court and a final judgment has issued that a question can arise as to whether, in order to protect the federal court's final judgment, it is necessary to enjoin state litigation of the issue "previously" decided by the federal court. In Chick Kam Choo , the Court was not called upon to decide whether a federal district court could enjoin ongoing state-court proceedings in which a state court had already issued an interlocutory ruling.

*147 The description in Chick Kam Choo of what § 2283 permits and does not permit was not intended to be all-encompassing. It is also important to recognize that in the very next sentence, the Supreme Court said that § 2283"is founded in the well-recognized concepts of res judicata and collateral estoppel," 12 as already noted.

The Supreme Court also said in Chick Kam Choo that "[t]he proper scope of the exception is perhaps best illustrated by this Court's decision in Atlantic Coast Line ." 13 The panel's opinion in the present case discusses that, in Atlantic Coast Line , a state-court injunction had been in effect for two years when the federal district court entered an order staying the state-court litigation. If a federal court has no authority under the Anti-Injunction Act to stay state-court proceedings once a state trial court has issued a ruling on the issue that is also presented to a federal court, then the Supreme Court could easily have vacated the federal injunction on that basis. It did not.

In Smith v. Bayer Corp. , the Supreme Court said, "[t]he Act's relitigation exception authorizes injunctions only when a former federal adjudication clearly precludes a state-court decision." 14 The Bayer decision, however, did not focus on whether the federal court's judgment had preceded the commencement of a state-court action or a ruling by a state court. The Court held that the federal court's stay was improper because "the issue presented in the state court was not identical to the one decided in the federal tribunal," and "the plaintiff in the state court did not have the requisite connection to the federal suit to be bound by the [federal court's] judgment." 15 The decision in Bayer recognized that "the Anti-Injunction Act's relitigation exception ... involves the requirement of preclusion law that a subsequent suit raise the 'same issue' as a previous case." 16 But here again, the relative points in time in which a federal court issued a decision and a state-court action was commenced were not at issue in Bayer , and the Court's general statement regarding the law of preclusion was imprecise. Preclusion law generally permits a final judgment to have preclusive effect when another court's ruling, even if prior in time, was not entitled to preclusive effect. 17

The Supreme Court has long recognized that state- and federal-court proceedings involving the same parties and issues may proceed, and often should proceed, on parallel tracks. 18 The Court's decision in Atlantic Coast Line said at one point that "the state and federal courts had concurrent jurisdiction in this case, and neither court was free to prevent either party from simultaneously pursuing claims in both courts." 19 But these are not holdings that when there are concurrent state- and federal-court proceedings, the federal court is powerless to protect or effectuate *148 its final judgment by staying further state-court proceedings. One of the decisions the Court cited in Atlantic Coast Line recognized that "Congress has seen fit to authorize courts of the United States to restrain state-court proceedings in some special circumstances," citing the Anti-Injunction Act, even though that decision also recognized that "where the judgment sought is strictly in personam, both the state court and the federal court, having concurrent jurisdiction, may proceed with the litigation at least until judgment is obtained in one of them which may be set up as res judicata in the other." 20

In Rivet v. Regions Bank of Louisiana , the Supreme Court signaled that a federal district court would have authority under the Anti-Injunction Act to enjoin state-court proceedings if necessary to protect or effectuate its judgment, even if that judgment had also been raised in a defensive plea in state court. 21 The Court's actual holding in Rivet was that "claim preclusion by reason of a prior federal judgment is a defensive plea that provides no basis for removal under § 1441(b)," and that "[s]uch a defense is properly made in the state proceedings, and the state courts' disposition of it is subject to this Court's ultimate review." 22 In a footnote appended to these statements, however, the Court said, "[w]e note also that under the relitigation exception to the Anti-Injunction Act, 28 U.S.C. § 2283 , a federal court may enjoin state-court proceedings 'where necessary ... to protect or effectuate its judgments.' " 23 On remand after the Supreme Court's decision in Rivet , the Fifth Circuit proceeded to address preclusion issues under Louisiana law in accordance with Parsons Steel, Inc. v. First Alabama Bank , 24 in deciding whether the federal district court had properly stayed proceedings under the Anti-Injunction Act. 25

There is no rationale expressed in any of the Supreme Court's decisions that supports differentiating how the Anti-Injunction Act is applied solely on the basis of whether a state court's ruling occurred before the federal district court issued a final judgment.

II

The majority opinion in the present case concludes that "[b]ecause Shaw assigned all of its interest in the litigation to Aptim, it is not apparent what litigation there is to continue in state court," and therefore that "Shaw's interest is moot." 26 As a consequence, the majority opinion affirms the district court's judgment in its entirety. With respect, I disagree with this disposition for at least two reasons.

First, the district court did not purport to resolve whether Shaw had waived its right to arbitrate disputes with McCall. Nothing in the district court's memorandum setting forth the reasons for its decision in this case addresses Shaw's right to arbitrate. After the district court entered its final judgment, McCall filed a "Motion to Stay Order and Judgment Pending Appeal." In the order denying this motion, the district court confirmed that its conclusion *149 that Aptim is entitled to an order compelling arbitration did not consider whether Shaw's actions were imputed to Aptim under Louisiana law regarding assignments, and that since McCall had not raised that argument in the district court initially, it was waived. 27 The district court also observed in the order denying a stay pending appeal that in any event, Aptim was joined as an additional party in state court and not substituted for Shaw. McCall had opposed substituting Aptim for Shaw in state court. The federal district court reasoned that "[i]t is therefore difficult for this Court to say that Aptim should now be held accountable for Shaw's actions when Defendant opposed a substitution and such was never actually made." Shaw was not a party to the federal district court suit, and the district court did not adjudicate whether Shaw was entitled to arbitrate claims against McCall.

The Supreme Court has made clear that a federal district court can stay a state-court action only as to issues actually determined by the federal district court. 28 In Chick Kam Choo , the Court discussed its decision in Atlantic Coast Line 29 to illustrate this principle, observing that "[t]he Court assessed the precise state of the record and what the earlier federal order actually said; it did not permit the District Court to render a post hoc judgment as to what the order was intended to say." 30 In the present case, the district court neither actually addressed Shaw's right to arbitrate nor whether the state-court proceeding was moot.

Second, it does not appear that the state-court proceedings are moot as to Shaw. In this court, McCall attached exhibits to a motion for stay pending appeal. One of those exhibits is a filing in the state-court action that asserts that McCall's claims against Shaw in state court include a claim for damages against Shaw for tortious interference with McCall's contract with Allied. 31

For these reasons, I would vacate the portion of the district court's judgment issuing a stay that appears to include Shaw as "an entit[y] in privity with" Aptim. I would otherwise affirm the district court's judgment.