Karl Kirsch and Susan Redden, defendants in the proceedings below, appeal from the district court’s 2 amended judgment granting summary judgment in their favor on all of the plaintiffs’ claims, but dismissing without prejudice the defendants’ counterclaims for indemnification. Kirsch and Redden argue the district court erred in dismissing their indemnification counterclaims by declining to retain supplemental jurisdiction over the counterclaims in response to the plaintiffs’ “motion for rehearing or relief from judgment” when the district court had previously entered judgment on the indemnification counterclaims in favor of defendants Kirsch and Redden. We affirm.
I. Background
Dennis Meier, Gwen Hougdahl, Kirsch, and Redden were at one time shareholders and employees of Innovative Home Health Care, Inc., a South Dakota corporation. After initiation of an action to dissolve the corporation, these individuals reached a settlement agreement. Subsequent to this agreement, Meier, Hougdahl, and Innovative Home Health Care, Inc., filed an action against Kirsch, Redden, a South Dakota corporation, and a general partnership, alleging violations of the Sherman Act, 15 U.S.C. §§ 1 & 2, and the Clayton Act, 15 U.S.C. §§ 15 & 26, as well as state claims of breach of contract and tortious interference with a contractual relationship. The defendants filed counterclaims against the plaintiffs, alleging breach of the settlement agreement and seeking indemnification for all reasonable costs and expenses incurred in defending the lawsuit based upon the terms of the settlement agreement.
The district court granted the defendants’ motion for summary judgment on all of the plaintiffs’ claims and on the defendants’ counterclaims, and entered judgment accordingly. As to the defendants’ indemnification counterclaims, the district court found that plaintiffs Meier and Hougdahl failed to “combat defendants’ showing” that the express language of the indemnification clause contained in the settlement agreement provided for indemnification.
The plaintiffs then filed a “motion for rehearing or relief from judgment” pursuant to Fed.R.Civ.P. 59(a) and 60(b)(6), arguing that the defendants were not entitled to relief on their indemnification counterclaims because the defendants simply relied on the language of the indemnification clause itself in support of their motion for summary judgment. Under such circumstances, the plaintiffs argued they were not required to present any opposing evidentiary matter in response to the defendants’ motion for summary judgment on the indemnification counterclaims. The plaintiffs also argued that, under South Dakota law, a written contract of indemnity will not be construed to indemnify a party against its own misconduct in the absence of a clear and unequivocal expression of such intent within the four corners of the contract.
In resolving the plaintiffs’ motion for rehearing, the district court noted that, after a year of discovery, the facts necessary for resolution of the plaintiffs’ state claims and the defendants’ counterclaim for breach of contract had been developed in the adjudication of the antitrust claim and such facts were intertwined with the federal antitrust claim. However, the court declined to retain jurisdiction over the defendants’ counterclaims for indemnification under 28 U.S.C. § 1367, stating:
Based on the parties’ recent submissions on the counterclaims for indemnification, the Court deems it necessary in serving the interests of justice to revisit its prior *1286decision to retain jurisdiction under 28 U.S.C. § 1367---- As previously noted in its memorandum opinion, the Court has broad discretion to dismiss state law claims and counterclaims over which it has only supplemental jurisdiction if the Court has dismissed all claims over which the Court had original jurisdiction which has occurred in this case.
The district court also noted that the parties’ submissions regarding the plaintiffs’ motion for rehearing raised “somewhat novel and complex issues of South Dakota law” regarding whether application of the indemnification clause under the facts and circumstances presented by this ease violated South Dakota law and whether the defendants could now also seek indemnification from the plaintiff corporation. The district court stated that determination of such issues would require further briefing and possible discovery.
The district court then amended its prior judgment by dismissing the defendants’ counterclaims for indemnification without prejudice. Defendants Kirsch and Redden appeal the amended judgment.
II. Standard of Review
Although the plaintiffs brought their motion for rehearing or relief from judgment pursuant to Fed.R.Civ.P. 59(a) and 60(b)(6), the plaintiffs properly concede the motion was actually an improperly styled Fed. R.Civ.P. 59(e) motion. Norman v. Arkansas Dep’t of Educ., 79 F.3d 748, 750 (8th Cir. 1996) (any motion questioning the correctness of a judgment is functionally a Fed. R.Civ.P. 59(e) motion, regardless of how the motion is styled); BBCA, Inc. v. United States, 954 F.2d 1429, 1432 (8th Cir.) (motion seeking substantive change in judgment was Rule 59(e) motion; substance, rather than form, of motion controls), cert. denied, 506 U.S. 866, 113 S.Ct. 192, 121 L.Ed.2d 136 (1992).
“‘A district court has broad discretion in determining whether to grant a [Fed. R.Civ.P. 59(e) ] motion to alter or amend judgment, and this court will not reverse absent a clear abuse of discretion.’ ” Global Network Techs., Inc. v. Regional Airport Autk, 122 F.3d 661, 665 (8th Cir.1997) (quoting Hagerman v. Yukon Energy Corp., 839 F.2d 407, 413 (8th Cir.), cert. denied, 488 U.S. 820, 109 S.Ct. 63, 102 L.Ed.2d 40 (1988)). “ ‘An abuse of discretion will only be found if the district court’s judgment was based on clearly erroneous factual findings or erroneous legal conclusions.’ ” Perkins v. U S West Communications, 138 F.3d 336, 340 (8th Cir. 1998) (quoting Mathenia v. Delo, 99 F.3d 1476, 1480 (8th Cir.1996), cert. denied, — U.S.-, 117 S.Ct. 2518, 138 L.Ed.2d 1020 (1997)).
III. Discussion
Federal Rule of Civil Procedure 59(e) was adopted to clarify a district court’s power to correct its own mistakes in the time period immediately following entry of judgment. Norman, 79 F.3d at 750 (citing White v. New Hampshire Dep’t of Employment Sec., 455 U.S. 445, 102 S.Ct. 1162, 71 L.Ed.2d 325 (1982)). Rule 59(e) motions serve a limited function of correcting “ ‘manifest errors of law or fact or to present newly discovered evidence.’” Hagerman, 839 F.2d at 414 (quoting Rothwell Cotton Co. v. Rosenthal & Co., 827 F.2d 246, 251 (7th Cir.), as amended, 835 F.2d 710 (7th Cir.1987)). Such motions cannot be used to introduce new evidence, tender new legal theories, or raise arguments which could have been offered or raised prior to entry of judgment. Id. A case in which a timely Rule 59(e) motion has been filed lacks finality because the motion tolls the time limitation for appeal in order to provide the trial court with jurisdiction to resolve the motion. This “tolling process” encourages “both correctness and finality.” Jackson v. Schoemehl, 788 F.2d 1296, 1298 (8th Cir. 1986). See also Sanders v. Clemco Indus., 862 F.2d 161, 170 (8th Cir.1988); 11 Charles Alan Wright, Arthur R. Miller & Mary Kay Kane, Federal Practice and Procedure § 2821, at 220-21 (2d ed.1995).
Relying on Villegas v. Princeton Farms, Inc., 893 F.2d 919 (7th Cir.1990), defendants Kirsch and Redden argue the district court erred in entering final judgment in their favor on the indemnification counterclaims, and then vacating that decision by dismissing the counterclaims without *1287prejudice upon consideration of the Fed. R.Civ.P. 59(e) motion filed by plaintiffs Meier and Hougdahl.
In Villegas, the district court granted the defendant’s motion to dismiss pursuant to Fed.R.Civ.P. 12(b)(6) because state law did not recognize the cause of action brought by the plaintiff, and entered judgment accordingly. The district court then granted the plaintiffs motion to vacate the judgment and voluntarily dismiss the case without prejudice, inviting the plaintiff to refile his action in state court. The Court of Appeals reversed the latter order, finding “a clear abuse of discretion to decide the merits of the legal issue while hearing the ease under diversity jurisdiction and then later redirect the parties to state court.” Id. at 923. The Villegas court stated that vacation of a judgment is authorized by Fed.R.Civ.P. 59(e), but “[i]n this ease, ... the district judge cited no errors or changes of heart regarding the merits of the legal arguments, but instead decided to send the ease to the Illinois courts as the preferred forum.” Id. at 924.
Villegas is readily distinguishable from the case before us because the district judge in this case expressly cited “errors or changes of heart regarding the merits of the legal arguments” related to the indemnification counterclaims and the merits of its prior decision to retain jurisdiction over those counterclaims pursuant to 28 U.S.C. § 1367. Specifically, the complexity of the state law issues involved in resolving the counterclaims, combined with the fact that the court had previously dismissed all claims over which it had original jurisdiction, led the court to reconsider its decision to retain supplemental jurisdiction—a proper use of Fed. R.Civ.P. 59(e) under Villegas and under the manifest-error-of-law standard in this circuit.
Section 1367 provides for the mandatory exercise of supplemental jurisdiction as follows:
Except as provided in subsections (b) and (c) or as expressly provided otherwise by Federal statute, in any civil action of which the district courts have original jurisdiction, the district courts shall have supplemental jurisdiction over all other claims that are so related to claims in the action within such original jurisdiction that they form part of the same case or controversy under Article III of the United States Constitution. Such supplemental jurisdiction shall include claims that involve the joinder or intervention of additional parties.
28 U.S.C. § 1367(a) (1993). Subsection (c) provides exceptions to the above mandatory command, granting district courts discretion to reject supplemental jurisdiction if:
(1) the claim raises a novel or complex issue of State law,
(2) the claim substantially predominates over the claim or claims over which the district court has original jurisdiction,
(3) the district court has dismissed all claims over which it has original jurisdiction, or
(4) in exceptional circumstances, there are other compelling reasons for declining jurisdiction.
28 U.S.C. § 1367(c). This subsection “plainly allows the district court to reject jurisdiction over supplemental claims only in the four instances described therein.” McLaurin v. Prater, 30 F.3d 982, 985 (8th Cir.1994).
While the district court’s power to exercise jurisdiction under the “same case or controversy” requirement in 28 U.S.C. § 1367(a) is one ordinarily resolved on the pleadings, the court’s decision to exercise that jurisdiction “is one which remains open throughout the litigation.” United Mine Workers v. Gibbs, 383 U.S. 715, 727, 86 S.Ct. 1130, 1139-40, 16 L.Ed.2d 218 (1966) (discus sion of pendent jurisdiction and discretionary power of federal trial court to refuse to hear state law claims, now codified by 28 U.S.C. § 1367).
Assuming the defendants’ state law indemnification counterclaims were sufficiently related to the plaintiffs’ jurisdictionally sufficient claims such that all claims could fairly be characterized as part of the “same case or controversy” pursuant to 28 U.S.C. § 1367(a), the district court had the discretion to decline to retain jurisdiction under section 1367(c)(3) (dismissal of all claims over which it had original jurisdiction) and 1367(c)(1) (complex issue of state law) at any *1288time in the litigation. Further, because the timely filing of the Rule 59(e) motion tolled the appeal time in order to provide the district court with jurisdiction to resolve the motion, the district court’s decision to relinquish supplemental jurisdiction was made before the case was “final” for appeal purposes.
Defendants Kirsch and Redden contend the district court’s reversal of its decision to retain supplemental jurisdiction violates the law-of-the-case doctrine. However, none of the cases on which Kirsch and Redden rely involve a district court’s decision to relinquish supplemental jurisdiction pursuant to 28 U.S.C. § 1367 in the context of resolving a Fed.R.Civ.P. 59(e) motion. LaShawn A. v. Barry, 87 F.3d 1389 (D.C.Cir.1996); Starks v. Rent-A-Center, 58 F.3d 358 (8th Cir.1995); Lovett v. General Motors Corp., 975 F.2d 518 (8th Cir.1992), cert. denied, 510 U.S. 1113, 114 S.Ct. 1058, 127 L.Ed.2d 378 (1994). In any event, a court has the power to revisit its prior decisions when “the initial decision was ‘clearly erroneous and would work a manifest injustice.’ ” Starks, 58 F.3d at 364 (quoting Christianson v. Colt Indus.Operating Corp., 486 U.S. 800, 817, 108 S.Ct. 2166, 100 L.Ed.2d 811 (1988)). As determined above, this is such a case.
IV. Conclusion
Upon further reflection and research regarding the defendants’ indemnification counterclaims prompted by the plaintiffs’ Rule 59(e) motion, the district court discovered that it had erred in granting summary judgment for the defendants on those counterclaims because complex issues of state law needed to be addressed through additional discovery and briefing before resolution of the indemnification counterclaims was possible. Thus, the district court sought to correct its error of law by relinquishing supplemental jurisdiction under 28 U.S.C. § 1367(e) for reasons expressly permitted therein—a complex issue of state law and dismissal of all claims over which the district court had original jurisdiction. Therefore, we cannot say the district court clearly abused its discretion in granting the plaintiffs’ motion pursuant to Fed.R.Civ.P. 59(e) and dismissing the indemnification counterclaims without prejudice.
Affirmed.
. The Honorable Richard H. Battey, Chief Judge, United States District Court for the District of South Dakota.