The parties are engaged in a dizzying web of interrelated lawsuits. It is therefore unfortunate, yet understandable, that in denying plaintiff’s request for an injunction that would have yielded finality, the district court relied on clearly erroneous factual assumptions. Lacking guidance from this court’s jurisprudence, the district court further misapplied applicable Supreme Court precedent in exercising its discretion. Regrettably, therefore, we reverse and remand, thereby allowing the wheels of justice to continue spinning a bit longer.

I.

The facts and proceedings are aptly described in our prior opinion, 1 so we only briefly summarize the relevant history here. Plaintiff Energy Development Corporation (“EDO”) and defendants Michael St. Martin, Virginia Rayne St. Martin, and *954 Quality Environmental Processes, Inc. (collectively, “the St. Martin Group” or “SMG”) have been engaged in a longstanding dispute over the mineral rights to a particular oilfield (the Sunrise Field) in Terrebonne Parish, Louisiana.

We greatly oversimplify by stating that SMG is the surface owner of the disputed tracts, and EDC claims mineral rights to much of the disputed land under a purported mineral servitude granted to its predecessors in 1971. SMG, for its part, also claims ownership of the minerals underlying the land. The crux of the dispute goes to whether the 1971 conveyance resulted in a valid servitude that extends to the present or whether, instead, SMG’s claim is superior.

A.

In 1998, EDC sued for a declaratory judgment establishing its mineral rights with respect to a portion of the disputed property (“the federal case”). The suit was later consolidated with an action brought when a mineral lessee of EDC and SMG deposited with the district court payments due under the leases and inter-pleaded EDC and SMG. A bench trial was held in May 2000 before Judge Schwartz, 2 who, in December 2000, granted EDC a declaratory judgment that we affirmed in the aforementioned opinion.

B.

In 1997, EDC sued in state court (Jefferson Parish), seeking a declaratory judgment that it had a valid mineral servitude on a tract of land neighboring the one at issue in the federal case, a tract of land also owned by SMG. Although that case involved a separate tract of land, it hinged on the same factual and legal issues relating to the validity of EDC’s mineral servitude.

The state court entered summary judgment for SMG in 1998, but that judgment was reversed and remanded for trial. Energy Dev. Corp. v. Quality Envtl. Processes, Inc., 734 So.2d 965 (La.App. 5th Cir. 1999). On remand, the trial court found that EDC did not have a valid mineral servitude and in 1999 entered judgment in favor of SMG in December 1999. The Court of Appeal affirmed on December 12, 2000 — just eight days before the federal district court issued its opinion and just over a month before it entered judgment. The Louisiana Supreme Court denied EDC’s application for writs on March 9, 2001. 3

After judgment was entered in state court — an act with preclusive effect under Louisiana law 4 — SMG did not raise the *955 issue of res judicata with the district court, but rather waited until its appeal to this court to raise the defense, arguing that the state ruling was not binding for res judicata purposes until after all appeals had been exhausted. Energy Dev. Corp., 296 F.3d at 361. This court rejected that argument and held that SMG’s res judicata argument was not properly before the court, because it had been waived by SMG’s not raising it in the federal district court. Id. We further opined, in dictum, that the state case would not be issue-preclusive of the federal case, because its ruling on the validity of the purported mineral servitude conveyance was not essential to its decision. Id. at 362. We therefore affirmed.

C.

While all this was transpiring, three related suits sprang up in the Louisiana courts. In September 1998, the lessees of EDC and SMG brought a concursus proceeding (the Louisiana equivalent to a federal interpleader action) (“the first concursus”) in state court (Terrebonne Parish), involving yet another tract of land in dispute between the parties — not the same portion of land at issue in the Jefferson Parish case or the tracts adjudicated in the federal case. Although the trial court initially found in favor of EDC, the Louisiana Court of Appeal remanded for consideration of SMG’s res judicata claim based on the Jefferson Parish judgment. Mandalay Oil & Gas, LLC v. Energy Dev. Corp., 867 So.2d 709, 2002 WL 1434422 (La.App. 1st Cir. July 3, 2002). 5

On remand, the trial court reversed course, finding that the Jefferson Parish judgment was preclusive of the first concursus in that, despite involving different areas of land, the Jefferson Parish decision was based on the same factual and legal disputes as that at issue in the first concursus. EDC appealed, and recently, after briefing in the instant appeal was complete, the Louisiana Court of Appeal affirmed the trial court’s decision granting judgment to SMG on grounds of res judicata. Mandalay Oil & Gas, LLC v. Energy Dev. Corp., 880 So.2d 129, 2004 WL 1737466 (La.App. 1st Cir. Aug.4, 2004).

To recap, at this point, with the parties having conclusively litigated their rights to three separate neighboring tracts of land in three different courts (two state and one federal) that had considered nearly identical legal and factual disputes, one court (the federal court) had found in favor of EDC, and the two state courts had ruled for SMG. Thus, although there are inconsistencies between the factual and legal conclusions of the federal court and those of the two state courts, the cases involved different tracts of land, and thus the judgments were not incapable of being honored simultaneously. 6 The matter becomes, however, more confusing.

D.

Regarding the so-called “collateral attacks,” 7 the lessees of EDC and SMG, on *956 May 23, 2000 — four days after the trial in the federal case came to a close but before the district court’s opinion was released or judgment entered — filed another concursus proceeding in Terrebonne Parish (the “first collateral attack”). This suit pitted EDC and SMG against each other as claimants to a disputed sum. The only difference in parties between that suit (as well as the second collateral attack, discussed infra) and the federal case is that the stakeholders who initiated the concursus and interpleader actions were different.

Importantly, the land at issue in the first collateral attack is wholly within the area adjudicated by the federal court. That is, a victory for SMG in this attack would be physically irreconcilable with the federal judgment. EDC and SMG filed cross-motions for summary judgment; EDC argued that the federal case rendered the concursus res judicata, and SMG urged that the Jefferson Parish case had preclusive effect and required a judgment on their behalf.

On June 30, 2003, the Terrebonne Parish court granted EDC’s motion for summary judgment and ruled against SMG, finding that the federal case has res judicata effect over the concursus action. SMG has appealed that decision to the Louisiana First Circuit Court of Appeal, where it pends. 8

Shortly after filing the first collateral attack, the parties’ lessees filed yet another concursus action (actually two that have been consolidated) (the “second collateral attack”) in Terrebonne Parish, again naming EDC and SMG as competing claimants to revenues from disputed lands, among which are several tracts that are within the lands the mineral rights to which were awarded to EDC in the federal case. Again, therefore, a judgment for SMG in the second collateral attack would create irreconcilable federal and state judgments that the parties could not possibly harmonize.

Not surprisingly, the parties have filed cross-motions for summary judgment, with EDC urging that the federal case be given preclusive effect and SMG arguing that the Jefferson Parish case should render the concursus res judicata. As of the briefing of this case, the Terrebonne Parish trial court had not ruled on these motions.

E.

Fearing the potentially irreconcilable conflicts that could result from an adverse decision in the first or second collateral attack, EDC in October 2003 moved the district court for a preliminary injunction prohibiting SMG from pursuing the first and second collateral attacks, ordering SMG to dismiss its appeal in the first collateral attack, and directing SMG to *957 dismiss its claims in the second collateral attack. EDC argued that the collateral attacks were res judicata as a result of the federal case and therefore must be enjoined.

EDC acknowledged that although the All Writs Act, 28 U.S.C. § 1651, authorizes the court to issue such an injunction, its power is sharply circumscribed by the Anti-Injunction Act, 28 U.S.C. § 2288, which prohibits federal courts from enjoining state court proceedings except in- three narrowly tailored situations: (i) where expressly authorized by an act of Congress, (ii) where necessary in aid of its jurisdiction, or (iii) to protect or effectuate its judgments (commonly known as the “relitigation exception”). EDC argued, and continues to urge on appeal, that all three exceptions apply, so the district court is entitled to grant the injunction it requests.

The district court denied EDC’s motion, Energy Dev. Corp. v. St. Martin, 2004 WL 117606, at *7 (E.D.La. Jan.23, 2004), deciding that, although the relitigation exception undoubtedly applies, the court, in the exercise of its broad discretion with respect to issuing injunctions, would not do so here. EDC appeals that denial.

II.

A.

Application of the exceptions to the Anti-Injunction Act is reviewed de novo 9 but the decision to grant or deny a preliminary injunction lies within the sound discretion of the district court, and that decision will be reversed only on abuse of discretion. 10 In exercising its discretion, the district court inevitably makes preliminary factual determinations and conclusions of law. 11 Those factual findings are reviewed for clear error, the legal conclusions de novo. 12 Where a denial of an injunction is based on clearly erroneous factual bases or incorrect application of law to facts, a district court has abused its discretion. 13

B.

In its explanatory order, the district court referred to the first concursus in Terrebonne Parish, which, in reality, dealt with land that does not overlap'with the land at issue in the federal case. Nevertheless, the court described this action as “involving, again, tracts of land the mineral rights to which were later adjudicated by the federal case to belong to EDC.” Energy Dev. Corp., 2004 WL 117606, at *2. This is a clearly erroneous statement of fact. Although EDC makes much of this in its brief, SMG does not attempt to refute EDC’s arguments.

This factual misunderstanding, by itself, would not be significant. After all, EDC is not now trying to enjoin the first concursus proceeding. Unfortunately, however, in calculating whether to issue the requested injunction, the district court found this “fact” significant. Denying the request for an injunction, the district court concluded,

*958 [S]hould the Louisiana First Judicial Circuit Court of Appeal or the Louisiana Supreme Court decide that the federal judgment is not claim preclusive as to the first collateral attack and the [first concursus], then this Court’s decision to enjoin the second collateral proceeding under the relitigation exception would cause a permanent inconsistency in the judgments of the three proceedings.

Id. at *4. It is apparent, from the order, that this fear of inconsistency was central to the court’s logic in denying the injunction.

As EDC points out, however, though the decision in the first concursus is legally inconsistent with the logic underpinning the federal case, the two are not physically inconsistent. Because the two judgments affect different tracts of land, the parties are perfectly capable of respecting both judgments simultaneously. As EDC puts it, “EDC can enjoy its servitude on the federal property while the St. Martin Group simultaneously enjoys its servitude over the property covered by the first concursus.” Although it may not be an abuse of discretion to deny the injunction sought by EDC, denying it based on a clearly erroneous finding of fact that obviously was significant to the court’s disposition of the case does constitute such an abuse.

C.

As we have said, the Anti-Injunction Act precludes federal courts from staying proceedings in state courts except where the case falls into one of the three narrowly-tailored statutory exceptions. 28 U.S.C. § 2283. 14 Only where (i) expressly authorized by statute, where (ii) necessary to aid the court’s jurisdiction, or (iii) to protect or effectuate its judgments may a federal court proceed with the extraordinary step of enjoining a state court action. At the district court and again on appeal, EDC urges that all three of these exceptions apply.

The district court unambiguously ruled that the third exception (commonly known as the “relitigation exception”) applies. Energy Dev. Corp., 2004 WL 117606, at *4. The court did not, however, make explicit findings with respect to the other two exceptions. The court noted that “[although EDC argued in brief that all three exceptions applied and Defendants argued in brief that none of the exceptions apply, both parties focused in oral argument on the relitigation exception. The Court finds that to be the appropriate exception to consider.” Id. at *3. But, as SMG concedes, the district court “simply chose to focus on the relitigation exception at oral argument,” rather than EDC steering the discussion in that direction. In any case, the order does not analyze the other two exceptions.

Such failure to address EDC’s argument was not reversible error. After all, only one of the exceptions need apply, and therefore, because the district court held that the relitigation exception applies, yet declined to issue the injunction, it did not matter whether the other two exceptions apply. Nevertheless, the parties expend significant energy arguing whether we should find those exceptions to apply. We decline the invitation and, instead, invite the district court to weigh in on those issues on remand.

*959 The district court did rule, on the other hand, with respect to the relitigation exception — specifically, holding that it undoubtedly applies. We agree.

SMG argues strenuously that the relitigation exception, “grounded in principles of res judicata and collateral estoppel,” 15 cannot apply to the collateral attacks because there is not exact similarity of parties among those cases and the federal case. For res judicata (and thus the relitigation exception) to apply, four elements must be present:

(1) [T]he parties in a later action must be identical to (or at least in privity with) the parties in a prior action; (2) the judgment in the prior action must have been rendered by a court of competent jurisdiction; (3) the prior action must have concluded with a final judgment on the merits; and (4) the same claim or cause of action must be involved in both suits.

Regions Bank v. Rivet, 224 F.3d 483, 488 (5th Cir. 2000) (internal quotation marks and citations omitted).

SMG weakly argues that EDC cannot make such a showing because the suits do not involve the same parties in that the petitioners (the stakeholders as opposed to the claimants) in the concursus are different from the stakeholders who initiated the federal interpleader action. 16 In reality, the additional parties, Mandalay Oil & Gas and Voyager Petroleum (lessees of the parties to this suit), are mere stakeholders in the concursus proceedings; the competing claimants (the same parties as in this suit) are the real parties in interest. Thus, the inclusion of the additional parties in the captions of the concursus proceedings is not sufficient to defeat the identity of the parties for res judicata purposes.

Moreover, Voyager and Mandalay are successors in interest to Louisiana Land and Exploration Company (“LL & E”), the stakeholder in the federal interpleader action that was consolidated with the federal declaratory action that formed the basis of the federal judgment. 17 Thus, as LL & E’s successors in interest, they are deemed to be in privity with LL & E, and there is therefore identity of the parties for res judicata purposes. As a result, the district court was correct to hold that the relitigation exception to the Anti-Injunction Act applies.

D.

Even though it held that the relitigation exception applies, the district court declined to issue an injunction, concluding that Parsons Steel v. First Ala. Bank, 474 U.S. 518, 106 S.Ct. 768, 88 L.Ed.2d 877 (1986), precluded it from doing so, at least with respect to the first collateral attack (in which the trial court had already ruled on the res judicata issue). In Parsons Steel, the Court considered whether a federal court could enjoin the enforcement of a state court judgment where the state court had already rejected a res judicata claim. Id. The Court held that even where a federal court found that res judicata should bar a parallel state court action (i.e., the relitigation exception applies), an injunction may not issue “[o]nce the state *960 court has finally rejected a claim of res judicata....’’ Id. at 524, 106 S.Ct. 768. Issuing an injunction in such a circumstance would violate the Full Faith and Credit Act, which provides that state court proceedings “shall have the same full faith and credit [in federal court] as they have by law or usage in the courts of such State ... from which they are taken.” 28 U.S.C. § 1738. Accordingly, “a federal court must give the same preclusive effect to a state-court judgment as another court of that State would give.” Parsons Steel, 474 U.S. at 523, 106 S.Ct. 768.

The district court believed that Parsons Steel barred it from issuing the requested injunction, at least with respect to the first collateral attack. Energy Dev. Corp., 2004 WL 117606, at *4. Specifically, the court stated that the Full Faith and Credit Act “requires this Court to give the trial court’s decision, that the federal court decision is claim preclusive as to the first collateral proceeding, full faith and credit.” Id. The court had very little easelaw from this circuit interpreting and applying Parsons Steel to analogous situations from which to draw guidance, and we disagree with its decision.

The district court described Parsons Steel as precluding injunctions under the relitigation exception to instances where “the state court has yet to rule on a claim of res judicata based on the federal action.” Id. In reality, as noted above, the Court’s holding precludes issuing an injunction only where “the state court has finally rejected a claim of res judicata.... ’’Parsons Steel, 474 U.S. at 524, 106 S.Ct. 768 (emphasis added). As for the finality requirement, that determination must be made under state law, i.e., whether a Louisiana state court would view the res judicata determination of the trial court in the first collateral attack as final enough to be binding upon other state courts.

Because the answer to that question is not necessary to our judgment and was not sufficiently briefed, we decline to venture a guess. Notwithstanding finality, however, the state court in the first collateral attack did not even reject the argument that the federal case was claim preclusive over that action, but instead, the trial court in the first collateral attack embraced the argument. Granting an injunction under these circumstances would therefore not run afoul of the Full Faith and Credit Act or Parsons Steel. As a result, the district court’s denial of an injunction, based as it was upon an erroneous interpretation of applicable law, was an abuse of discretion.

E.

EDC contends that the district court further erred as a matter of law by failing to hold that the law of the case doctrine precludes SMG from pursuing collateral attacks in state court. According to EDC, this court in its July 2002 opinion conclusively determined that the Jefferson Parish judgment cannot have preclusive effect superior to that of the federal judgment. Therefore, goes the argument, SMG’s collateral attacks, in which it urges that the Jefferson Parish judgment requires victory in its favor, are themselves doomed to failure. That being the case, EDC believes it is all the more appropriate that the district court enjoin those proceedings.

This argument is unpersuasive. Not only is EDC incorrect in its characterization of our July 2002 opinion, but even if it were correct, that does not necessarily compel the district court to grant its request for an injunction.

In the July 2002 opinion, we declined SMG’s request to reverse the federal judgment on the ground that the Jefferson Parish judgment was preclusive. Energy *961 Dev. Corp., 296 F.3d at 361. SMG had not raised this argument at the district court and pursued it for the first time on appeal. Id. Because SMG failed to raise the argument in the district court, we “decline[d] to consider the defendants’ assertion of res judicata or collateral estoppel at this stage of the litigation.” Id. at 363.

Nevertheless, EDC continues to urge that “this Court necessarily found that the St. Martin Group’s res judicata motion failed on the merits.” This is incorrect. Because this court unambiguously determined that the res judicata claim was not properly before the court, any discussion of the merits of the argument is obvious dictum and cannot be relied on as the law of the case. 18

III.

As the parties’ briefs indicate, they are fully aware that the mere fact that an injunction may issue under the Anti-Injunction Act, does not necessarily require that the district court must issue the requested injunction. See Chick Kam Choo v. Exxon Corp., 486 U.S. 140, 108 S.Ct. 1684, 100 L.Ed.2d 127 (1988). On remand, the district may again, in its sound discretion, find that the extraordinary remedy of enjoining state court proceedings is inappropriate. Nevertheless, the district court’s decision to deny EDO’s request, based as it was on erroneous factual underpinnings and a misapplication of Supreme Court precedent, constituted an abuse of discretion.

In reconsidering its earlier denial of EDO’s request for an injunction, the district court must proceed with the understanding that the first concursus, although legally inconsistent with the federal judgment, is not physically inconsistent. Moreover, because the state court has not yet finally rejected EDO’s res judicata claim, Parsons Steel does not preclude the court from preventing a physically conflicting judgment in the first collateral attack.

As a result, the denial of EDO’s motion for preliminary injunction is REVERSED, and this matter is REMANDED for further proceedings consistent with this opinion.