The Procter & Gamble Company and the Procter & Gamble Distributing Company (jointly referred to in the singular as *498“P&G”) appeal a summary judgment in favor of defendant Amway Corporation, alleging that the district court gave improper res judicata effect to a judgment of the United States District Court for the District of Utah. Concluding that the Utah court’s judgment is entitled to res judicata effect, we affirm.
I.
The dispute between Procter & Gamble and Amway has been before this court on two prior occasions. See Procter & Gamble Co. v. Amway Corp., 242 F.3d 539 (5th Cir.2001) (“P&G I”); Procter & Gamble Co. v. Amway Corp., 280 F.3d 519 (5th Cir.2002) (“P&G II"). Because the complete factual history is set out in those opinions, we only summarize the relevant procedural history.
P&G has long been the subject of rumors linking it to Satanism and has attempted to identify Amway and its distributors as the source of those rumors. In 1995, P&G sued Amway and other defendants in federal district court in Utah. P&G then filed a second amended complaint alleging defamation, common law unfair competition, violations of the Utah Truth in Advertising Act, tortious interference, negligent supervision and violations of the Lanham Act, and vicarious liability arising out of the Satanism rumor. P&G later filed a third amended complaint alleging that Amway’s distribution method was an illegal pyramid scheme, and claiming fraud and product disparagement.
The Utah court granted Amway’s motion to dismiss the Third Amended Complaint. P&G later filed a Fourth Amended Complaint asserting claims for product disparagement, based on allegations that Amway had told consumers that P&G’s Crest toothpaste scratches teeth, and asserting fraud, but the Utah court dismissed that complaint as untimely filed.
Meanwhile, P&G sued in the United States District Court for the Southern District of Texas, alleging causes of action for unfair competition, negligent supervision, negligence, business disparagement, defamation, tortious interference with prospective business relations, vicarious liability, fraud, violations of RICO, violations of the Lanham Act, and violations of the Texas Business and Commerce Code. These causes of action were based on the Satanism rumor, the Crest rumor, and Amway’s alleged pyramid scheme. In April 1999, the Utah court entered a final judgment dismissing all of P&G’s claims.
The instant case went to trial in May 1999. At the close of P&G’s case, Amway moved for judgment as a matter of law. The district court granted the motion and dismissed P&G’s Lanham Act claim on the basis of the res judicata effect of the Utah court’s judgment. It also dismissed P&G’s remaining claims on the merits. After the Texas court had entered judgment, but before we heard the appeal, the Tenth Circuit affirmed in part, reversed in part, and remanded the Utah district court’s judgment. See Proctor & Gamble Co. v. Haugen, 222 F.3d 1262 (10th Cir.2000) 9“Haugen I").
In P&G I, we affirmed in part and reversed in part the district court’s rulings on the merits. Most importantly, we found that at the time P&G I was decided, there was no res judicata effect from the Utah case. We held that the district court had correctly accorded the Utah court’s judgment res judicata effect and that dismissal had been proper when granted. The Tenth Circuit’s subsequent reversal and remand eliminated, however, any res judicata bar occasioned by the reversed and remanded judgment. P&G I, 242 F.3d at 546. Accordingly, we vacated on the ground of res judicata.
*499The issues we considered in P&G II did not concern Amway or the appeal before us today. We did, however, note that after P&G I and P&G II, “the only claims currently before the district court relate to spreading the Satanism and Crest toothpaste rumors.” P&G II, 280 F.3d at 524.
On remand from the Tenth Circuit, the Utah court dismissed all of P&G’s claims. Procter & Gamble Co. v. Haugen, 158 F.Supp.2d 1286 (N.D.Utah 2001), aff'd, 317 F.3d 1121 (10th Cir.2003). Shortly after the Tenth Circuit’s affirmance, the Texas district court granted Amway’s motion for summary judgment, dismissing P&G’s remaining claims. P&G filed a timely notice of appeal, and the district court subsequently entered judgment pursuant to Fed.R.Civ.P. 54(b), thus assuring our jurisdiction over this appeal.
II.
We review a summary judgment de novo, using the same standards as did the district court. BP Oil Int’l, Ltd. v. Empresa Estatal Petoleos de Ecuador, 332 F.3d 333 (5th Cir.2003). The res judicata effect of the Utah judgment is a question of law that we also review de novo. P&G I, 242 F.3d at 546.
A.
Under the law of this circuit, “[cjlaim preclusion, or ‘pure’ res judicata, is the ‘venerable legal canon’ that insures the finality of judgments and thereby conserves judicial resources and protects litigants from multiple lawsuits.” United States v. Shanbaum, 10 F.3d 305 (5th Cir. 1994). Res judicata applies where “(1) the parties to both actions are identical (or at least in privity); (2) the judgment in the first action is rendered by a court of competent jurisdiction; (3) the first action concluded with a final judgment on the merits; and (4) the same claim or cause of action is involved in both suits.” Ellis v. Amex Life Ins. Co., 211 F.3d 935, 937 (5th Cir.2000). If these conditions are satisfied, all claims or defenses arising from a “common nucleus of operative facts” are merged or extinguished. Agrilectric Power Partners, Ltd. v. Gen. Elec. Co., 20 F.3d 663 (5th Cir. 1994).
In P&G I, 242 F.3d at 544, we noted that “[t]his suit is based on the same transactions, and involves substantially the same parties, as does the Utah suit.” Having already decided that res judicata based on the Utah court’s judgment in Haugen I would have been appropriate but for the fact that the judgment had been reversed and remanded, we now conclude that res judicata was appropriate based on the Utah court’s affirmed judgment on the merits in Haugen II. 1
*500P&G contends that the district court erred in according the Utah court’s judgment res judicata effect, alleging (1) that it was improperly based on the res judicata effect of the later-reversed opinion of the Texas court in P&G I, (2) that it was based on incorrect legal conclusions, contrary to those established in P&G I, and (3) that it was entered without giving P&G fair opportunity to be heard. P&G’s arguments amount to the contention, that the Utah court decided the case wrongly, or at least differently from how the Texas court would have done so under this circuit’s law.
P&G’s first allegation is faulty, inasmuch as the Tenth Circuit recognized the potential difficulty of the Utah court’s basing its decision on res judicata and proceeded to consider and affirm the Utah court’s decision on the merits. This, highlights a flaw in P&G’s argument: The proper remedy for an allegedly erroneous judgment is direct appeal to the proper court, not an attempt to avoid the res judicata effect of that judgment in another suit against the same party for the same cause of action.
All the issues P&G raises assert errors of law that would undermine the correctness of the Utah court’s judgment. The question whether that judgment on the merits was correct, however, does not enter into our inquiry on the subject of res judicata, for even an incorrect judgment is entitled to res judicata effect. See Parsons Steel, Inc. v. First Ala. Bank, 474 U.S. 518, 525, 106 S.Ct. 768, 88 L.Ed.2d 877 (1986).
“The general rule [of res judicata] stated in this Section requires that errors underlying a judgment be corrected on appeal or other available proceedings to modify the judgment or to set it aside, and not made the basis for a second action on the same claim.” Restatement (Second) of Judgments § 19 cmt. a (1982). As a learned treatise puts it, “[r]es judicata applies even if the next court to visit the dispute believes that the second court’s res judica-ta ruling was wrong.” 18 WRIGHT, Miller & CoopeR, Federal PRACTICE and Prooe-dure: JurisdiCtion 2d § 4404 (2d ed.2002). Even where the second court incorrectly gives preclusive effect to the first court’s judgment, the first court is bound by the res judicata effect of the second court’s judgment. In re Brady, Tex., Mun. Gas Corp., 936 F.2d 212 (5th Cir.1991).
When two suits proceed simultaneously, as in this case, res judicata effect is given to the first judgment rendered. Chicago, Rock Island & Pac. R.R. v. Schendel, 270 U.S. 611, 46 S.Ct. 420, 70 L.Ed. 757 (1926); see also 18 Wright, Miller & Cooper, supra, Jurisdiction 2d § 4404 (citing Jones v. Sheehan, Young & Culp, 82 F.3d 1334, 1338-39 n. 3. (5th Cir.1996); In re Hansler, 988 F.2d 35, 38 (5th Cir.1993)). Maintaining such a litigation strategy almost assures that at some point one of the cases will become barred by a judgment in the other; the successful party will find that all its claims and defenses have merged into the judgment, while the unsuccessful party will find that its have been extinguished. “There is no reason why defendants should be required to defend, or courts to hear, additional or multiple cases, free from the protections of res judicata, simply because the plaintiff chose to file them piecemeal at the same time rather than in succession.” Sidag Aktiengesellschaft v. Smoked Foods Prods. Co., 776 F.2d 1270 (5th Cir.1985). A party *501gets only “one bite at the apple” and is not allowed to take two bites simply because it attempts to take both at once rather than seriatim.
B.
P&G contends that, in according the Utah judgment res judicata effect, the district court improperly disregarded the law of the case as established by this court and slighted the mandate in P&G I. This objection is misguided. Nothing in our prior rulings has established that a valid judgment from the Utah court should not be given res judicata effect by the Texas court; quite to the contrary, we stated that the Texas court’s invocation of res judicata in P&G I was proper but for the fact that the Utah court’s decision was later reversed and remanded. It did not, therefore, run afoul of our mandate for the district court to accord the Utah judgment res judicata effect.
To the degree that the decisions of the Utah court and Tenth Circuit on particular issues may conflict with our holdings on those issues, P&G has identified a potential source of conflict between the application of collateral estoppel based on the Utah judgments and the law of the case or mandate of the Texas case. This difficulty does not arise, however, where res judica-ta operates not to determine issues within a case but to extinguish the ease as a whole.
Although law of the case and res judicata are somewhat related preclusive doctrines, “the law of the case doctrine is merely a rule of practice, based upon sound policy,” while “[r]es judicata ... is categoric and requires that respect be accorded the prior judgment.” Loumar, Inc. v. Smith, 698 F.2d 759, 762 (5th Cir. 1983). In discussing the relationship between the doctrines of law of the case and res judicata, the Supreme Court noted that “there is a difference between such adherence [to law of the case] and res judicata; one directs discretion, the other supersedes it and compels judgment. In other words, in one it is a question of power, in the other of submission.” S. R.R. v. Clift, 260 U.S. 316, 319, 43 S.Ct. 126, 67 L.Ed. 283 (1922). The application of res judicata in this case does not conflict with this court’s rulings or mandates on the merits of P&G’s claims. Rather, it bars them a priori.
The district court properly dismissed P&G’s claims. The judgment, accordingly, is AFFIRMED.