
575 F.3d 542 (2009)
Royal BENSON, MD; Benson OB/GYN Center, PA, Plaintiffs-Appellants,
v.
ST. JOSEPH REGIONAL HEALTH CENTER; St. Joseph Health System; Franciscan Services Corporation; Sisters of St. Francis of Sylvania, Ohio; Betty G. Acker, MD; Daniel Buche; Dr. Thomas W. Davis, Jr.; Dr. Daniel B. Dawson; Dr. David R. Doss; Dr. Robert H. Emmick, Jr.; Gretchen Kunz; Dr. G. Mark Montgomery; RN Myesha Nichols-Turner; Dr. William F. Price; Alan C. Smith; Kathleen A. Thomas, Defendants-Appellees.
No. 07-20726.
United States Court of Appeals, Fifth Circuit.
July 10, 2009.
*544 Gaines F. West (argued), West, Webb, Allbritton & Gentry, College Station, TX, for Plaintiffs-Appellants.
Robert L. Hargett, Davis & Wilkerson, Austin, TX, for St. Joseph Reg. Health Ctr., St. Joseph Health Sys., Franciscan Services Corp., Sisters of St. Francis of Sylvania, OH, Buche, Kunz, Montgomery, Nichols-Turner, Smith and Thomas.
Daryl G. Dursum (argued), Adams & Reese, Houston, TX, for Acker, Davis, Dawson, Doss, Emmick and Price.
Before KING, STEWART and SOUTHWICK, Circuit Judges.
LESLIE H. SOUTHWICK, Circuit Judge:
Dr. Royal Benson, a doctor specializing in obstetrics and gynecology, had his medical privileges terminated at the defendant hospital. He alleges that this occurred as a result of a malicious and unreasonable peer review. Benson sued the hospital and numerous individuals involved in the peer-review process. The district court granted summary judgment to all Defendants. For the reasons that follow, we affirm the judgment of the district court.

I. BACKGROUND
Benson joined the Brazos Valley Women's Center as an associate OB/GYN in 1992. Around the same time, he also obtained privileges to practice at St. Joseph Regional Health Center, a hospital between Bryan and College Station, Texas. The hospital grants clinical privileges on a two-year basis. Application for renewal of those privileges is required at the end of each term.
Appellees Betty Acker, David Doss, and Mark Montgomery practiced with Benson at the Center and also held privileges at St. Joseph. Benson contends that he worked at the Center until 1997, when he was voted out because of "personal animosity" held by the other doctors against him and because of his "desire to change the group's distribution of net profits." He opened his own practice after the separation and continued working at St. Joseph.
Benson's two-year contract at St. Joseph was up for renewal in September 2001. The month before his privileges were to expire, however, St. Joseph's Credentials Committee recommended that all OB/GYNs set for September reappointment receive a six-month extension while a team from the American College of Obstetricians and Gynecologists ("ACOG") conducted a review of the OB/GYN department. Benson was informed by letter that he had been approved for the six-month extension, pending the ACOG review.
The ACOG crew reviewed the OB/GYN department's quality of care over a four-day period in November 2001 and reported its findings in January 2002. St. Joseph's Credentials Committee then created an ad *545 hoc committee to review the ACOG report and make recommendations. Based on the ACOG report, the ad hoc committee provided the Credentials Committee with a recommendation not to renew Benson's privileges. Thereafter, the Credentials Committee provided that same recommendation to the Medical Executive Committee.
Prior to acting on the recommendation, the Executive Committee gave Benson an opportunity to address the criticisms contained in the ACOG report. He was unable to satisfy the Executive Committee, though, and a non-renewal recommendation was forwarded to the St. Joseph's Governance Council. Benson's hospital privileges expired on March 25, 2002.
Benson subsequently took advantage of his right to request a hearing on the Executive Committee's recommendation. Fourteen sessions were held between July 2002 and April 2003. At the end of the sessions, the Executive Committee again voted to recommend that Benson's privileges be revoked. Benson sought appellate review before St. Joseph's Governance Council.
In November 2004, while his internal review was pending, Benson filed suit in the U.S. District Court for the Southern District of Texas. Defendants were St. Joseph and several hospital employees who had participated in his peer review.[1] He alleged that the peer-review process was tainted by the participation of several doctors who previously worked with him at the Center, including Acker, Doss, and Montgomery. Benson sought damages in the form of lost profits for the time he was unable to practice at St. Joseph.
The Defendants answered, then later moved for summary judgment. The district court granted summary judgment with respect to the state claims on qualified immunity grounds and granted summary judgment with respect to a federal antitrust claim for a reason other than qualified immunity. The court denied all other motions as moot. Benson moved twice, unsuccessfully, to alter or amend the judgment. This appeal followed.

II. DISCUSSION

A. State Statutory Claims
The Texas Medical Practice Act ("TMPA") affords immunity from civil liability to peer-review participants when they act "without malice and in the reasonable belief that the action or recommendation is warranted by the facts known to that person." Tex. Occup. Code § 160.010(a)(2). The district court, on March 22, 2007, granted summary judgment against Benson on his state law claims after determining that the Defendants were entitled to the TMPA's immunity. In so holding, the district court explained that peer-review participants are always presumed to have acted without malice. It also found that, to overcome the presumption, a plaintiff bears the burden of proving the contrary by clear and convincing evidence.
Whether the district court was correct to employ the clear and convincing evidentiary standard is the question on the merits. Before we can review that point, however, it is necessary to evaluate whether the argument was properly preserved for our review. Puckett v. United States, ___ U.S. ___, 129 S.Ct. 1423, 1428, 173 *546 L.Ed.2d 266 (2009) (If a trial court error is not preserved, authority to correct the error on appeal "is strictly circumscribed.").
Following the summary judgment order, Benson filed a Motion to Alter or Amend Judgment on April 5, 2007, within the required ten-day period. See Fed.R.Civ.P. 59(e). In the motion, Benson did not argue that the district court's use of the clear and convincing standard was error. Instead, he maintained that the district court erred because substantial evidence was produced "that would permit a reasonable jury to conclude that Defendants acted with actual malice, and thus are not entitled to immunity under the TMPA." The district court denied the motion on August 22, 2007.
After the denial, Benson filed what he referred to as a Second Motion to Alter or Amend Judgment on September 6, 2007. Benson now did contest the district court's use of the clear and convincing standard, asserting that a preponderance of the evidence standard applied. The Defendants responded by arguing, first, that Benson's Rule 59(e) motion was successive, and in the alternative, that he was judicially estopped from making the argument.
Before the district court ruled on the motion, Benson filed a notice of appeal seeking review of the district court's summary judgment order and the denial of his first motion to alter or amend. The date of the notice of appeal was September 21, 2007.
On October 22, 2007, the district court evaluated Benson's September 6, 2007 motion. It did not address the untimeliness or successive nature of Benson's second Rule 59(e) motion. Rather, it denied Benson's motion on the ground that he was judicially estopped from arguing that an inappropriate evidentiary standard had been employed.
Following the district court's ruling, Benson filed an amended notice of appeal. This amendment was filed on November 8, 2007. It sought review of the district court's grant of summary judgment and of the denials of both motions to alter or amend the judgment.
We start with analyzing the effect of the filing of two motions under Rule 59(e). Only the first one tolled the thirty-day period for filing a notice of appeal. See Charles L.M. v. Ne. Indep. Sch. Dist., 884 F.2d 869, 870 (5th Cir.1989). Benson filed a notice of appeal on September 21, 2007, without waiting for a ruling on his second Rule 59(e) motion. That was wise, as it satisfied the requirement to file within thirty days of the district court's August 22 ruling denying the first Rule 59(e) motion. That notice of appeal brought to us all matters identified in the motion that had been properly presented to the district court prior to that time.
Unfortunately, Benson's principal argument on appeal  that the wrong evidentiary standard was applied  had not yet been presented to the district court by the time of the notice of appeal. On appeal, the Defendants raise that objection to consideration of the issue. They begin their response to the issue of the evidentiary standard by pointing out that the "only time [Benson] ever suggested the standard of proof under the TMPA should be something other than `clear and convincing' was after their First Motion to Alter or Amend was denied." In making this argument, the Defendants did not refer to waiver or a failure to preserve. Instead, they argued that Benson's argument in his Rule 59(e) motion that he had satisfied the clear and convincing standard was a "judicial admission" that conceded the issue. See Martinez v. Bally's La. Inc., 244 F.3d 474, 476 (5th Cir.2001). It is not that, as Benson never formally conceded the standard utilized *547 by the district court. Nonetheless, the Defendants have argued that Benson improperly waited to present his argument on the alleged error in the evidentiary standard until the second Rule 59(e) motion. We find the issue of the impropriety of the motion to be raised adequately.
The federal rules do not provide for a motion requesting a reconsideration of a denial of a reconsideration. Charles L.M., 884 F.2d at 870. Were such motions permitted, it is conceivable that a dissatisfied litigant could continually seek reconsideration and prevent finality to the judgment. Benson's first Rule 59(e) motion was timely, was considered and denied, and exhausted Benson's right to reconsideration. Our question, though, is tangential from the ones that we find to be answered by the precedents. We need to decide if a litigant has sufficiently presented to a district court an issue that only appears in an improper, successive Rule 59(e) motion.
A beginning to our needed answer is found in the fact that certain procedural flaws in Rule 59(e) motions are not fatal. This court has recognized that we "`may treat an untimely 59(e) motion to alter or amend the judgment as if it were a Rule 60(b) motion if the grounds asserted in support of the Rule 59(e) motion would also support Rule 60(b) relief.'" Halicki v. La. Casino Cruises, Inc., 151 F.3d 465, 470 (5th Cir.1998) (quoting 12 JAMES W. MOORE ET AL., MOORE'S FEDERAL PRACTICE § 60.03[4], at 60-24 (3d ed.1998)). We see no reason an improperly successive Rule 59(e) motion could not similarly be transformed into a Rule 60(b) motion. At least for purposes of our analysis today, we make that assumption.
Under Rule 60(b)(1), the court may grant relief from a final judgment or order on the grounds of "mistake, inadvertence, surprise, or excusable neglect," with "mistake" being the only possibly relevant ground here. The "mistake," though, was an alleged substantive legal error on the part of the district court. We now look to whether a legal error can be raised in a Rule 60(b) motion.
"The circuits are split concerning whether courts may reconsider, pursuant to Rule 60(b)(1), legal errors they may have made in a judgment." MOORE, supra, § 60.41[4][a], at 60-109. Our rule is that a Rule 60(b) motion may be used "to rectify an obvious error of law, apparent on the record." Hill v. McDermott, Inc., 827 F.2d 1040, 1043 (5th Cir.1987). If such is the purpose of the motion, the Rule 60(b) motion ordinarily must be filed within the time for taking an appeal.[2]Id. Our stated rationale has been that "a Rule 60(b)(1) motion filed within the time for appeal saves the parties and the court time and expense of a needless appeal." Id. Our focus on "obvious" legal error, which this court as a matter of course would correct anyway, is to prevent a Rule 60(b) motion from being used as a substitute for a timely appeal on disputed issues. Id.
Benson did file his successive motion within the time for taking an appeal. The district court denied the first Rule 59(e) motion on August 22, 2007. From that point, Benson had thirty days to file a notice of appeal. The successive motion was filed on September 6, 2007, well within the thirty-day time frame.
Though the motion was proper as to time, we find that it was not proper as to *548 subject. The alleged legal error is not one appropriately characterized as an "obvious error of law." See id. While we may doubt whether the district court employed the appropriate evidentiary standard,[3] all parties concede that Texas state courts have never expressly stated what standard should be used to prove malice in this context. Therefore, were we to reach the merits of Benson's claim, we would be required to determine how the Texas Supreme Court would interpret state law. See Beavers v. Metro. Life Ins. Co., 566 F.3d 436, 439 (5th Cir.2009). This is not the sort of legal error we have allowed to be brought in a Rule 60(b) motion. See Alvestad v. Monsanto, 671 F.2d 908, 913 (5th Cir.1982) (recognizing that our prior Rule 60(b) cases involving alleged legal errors have attempted "merely to avoid wasting appellate resources on the perfunctory correction of `obvious errors of law'"). The answer would not be free from doubt. Consequently, any error is not so obvious as to permit the impropriety of the motion to be overlooked.
We find that Benson's arguments are not entitled to be treated as an exception to the usual requirement that an issue must first be presented to the district court before it may be raised on appeal. AG Acceptance Corp. v. Veigel, 564 F.3d 695, 700 (5th Cir.2009). The alleged legal error in the district court's ruling could have been argued in the first, properly filed motion to alter or amend the judgment. The initial Rule 59(e) mechanism is a "readily available procedure[] by which a party may seek reconsideration by a court of a number of matters, including legal errors made by the court." MOORE, supra, § 60.41[4][a], at 60-109. Benson failed to utilize it.
It is true, though, that we may consider arguments concerning pure questions of law that were not presented to the district court. Veigel, 564 F.3d at 700. A plain-error standard of review is applied to determine if the procedural default can be overridden. Holmes v. Tex. A&M Univ., 145 F.3d 681, 685 (5th Cir.1998). The plain-error test requires that there be (1) an error; (2) that it be plain; (3) and that substantial rights be affected. Id.
The problem for Benson is, again, that any legal error as to the evidentiary standard was not plain. If the TMPA requires only that malice be proved by a preponderance of the evidence, then the district court's utilization of the clear and convincing standard was error. But that error may not be characterized as plain because, as we stated, the parties concede that Texas state courts have never made the standard clear. Indeed, at least one federal court applying Texas law has found that clear and convincing evidence is needed to rebut the presumption against malice. Jenkins v. Methodist Hosps. of Dallas, Inc., No. 3:02-cv-1823-M, 2004 WL 3393380 (N.D.Tex. Aug. 14, 2004) (unpublished).
Because Benson first raised the alleged legal error presented to this court in an improper second Rule 59(e) motion, it was not preserved for our review. The district court's grant of qualified immunity to the Defendants under the TMPA must therefore stand.

B. Federal Antitrust Claim
Our review of a summary judgment is de novo. Ahrens v. Perot Sys. Corp., 205 *549 F.3d 831, 833 (5th Cir.2000). "We view all facts in the light most favorable to the non-movant, and affirm only when the evidence `show[s] that there is no genuine issue as to any material fact and that the movant is entitled to judgment as a matter of law.'" Golden Bridge Tech., Inc. v. Motorola, Inc., 547 F.3d 266, 270 (5th Cir. 2008) (quoting Fed.R.Civ.P. 56(c)).
Section 1 of the Sherman Antitrust Act states: "Every contract, combination in the form of trust or otherwise, or conspiracy, in restraint of trade or commerce among the several States, or with foreign nations, is declared to be illegal." 15 U.S.C. § 1. To prove a claim, plaintiffs must demonstrate that "(1) the defendants engaged in a conspiracy; (2) that restrained trade; (3) in the relevant market." Golden Bridge Tech., Inc., 547 F.3d at 271. When there is no allegation that the alleged conspiracy is per se unreasonable, the plaintiff is required to demonstrate that the alleged conduct unreasonably restrains trade in light of actual market forces under the rule of reason. Id.
This rule of reason requires that a fact-finder consider "`all of the circumstances of a case in deciding whether a restrictive practice should be prohibited as imposing an unreasonable restraint on competition.'" Leegin Creative Leather Prods., Inc. v. PSKS, Inc., 551 U.S. 877, 127 S.Ct. 2705, 2712, 168 L.Ed.2d 623 (2007) (quoting Cont'l T.V., Inc. v. GTE Sylvania Inc., 433 U.S. 36, 49, 97 S.Ct. 2549, 53 L.Ed.2d 568 (1977)). A violation requires proof that the practice "actually had an adverse effect on competition." Tunica Web Adver. v. Tunica Casino Operators Ass'n, 496 F.3d 403, 412 (5th Cir. 2007). The court must balance the anticompetitive effects of the restrictive practice against any benefits or justifications within the relevant product and geographic markets. Doctor's Hosp. of Jefferson, Inc. v. Se. Med. Alliance, Inc., 123 F.3d 301, 307 (5th Cir.1997).
We apply these principles to Benson's claims. He maintains that the district court erred in determining that St. Joseph's refusal to renew his privileges did not adversely affect OB/GYN services in Brazos County. He points specifically to two anticompetitive effects: (1) reduction in consumer choice of providers and (2) reduction in consumer choice of services.
With respect to providers, Benson notes that there is only one other hospital besides St. Joseph that provides obstetrics and gynecology services in Brazos County. Further, the four major insurance plans available to consumers only include St. Joseph in their coverage area. His ultimate point is that patients "desiring to receive treatment from Dr. Benson were forced to use other facilities in the county, which required prohibitive out of pocket costs."
With respect to services, Benson asserts that he "offered unique services and procedures that no other OB/GYN could have provided" in Brazos County. He also maintains that no other doctor performed certain specialized services that he identifies. "Patients seeking these specialized services were forced to go elsewhere while Dr. Benson was not privileged at [St. Joseph]."
We agree with the district court that Benson has not raised a genuine issue of material fact on this issue. Benson's privileges were not renewed at St. Joseph for a period of more than three years. Still, he was free to provide services at his own clinic in Brazos County. The inability to service patients at the hospital of his choice does not demonstrate an unreasonable adverse impact on OB/GYN services for the entire county. See Doctor's Hosp. *550 of Jefferson, Inc., 123 F.3d at 309; see also BCB Anesthesia Care, Ltd. v. Passavant Mem'l Area, 36 F.3d 664, 667-68 (7th Cir. 1994) (collecting rule of reason cases and noting that "[t]hose hundreds or thousands of pages almost always come to the same conclusion: the staffing decision at a single hospital was not a violation of section 1 of the Sherman Act"). Hence, Benson's antitrust claim fails as a matter of law.

C. Leave to Amend
Benson also challenges the district court's denial of his motion to amend his pleadings, in which he attempted to add a breach of contract claim that he contends falls outside the ambit of the Defendants' qualified immunity. Our review of the district court's denial of leave to amend a complaint is for abuse of discretion. Cent. Laborer's Pension Fund v. Integrated Elec. Servs. Inc., 497 F.3d 546, 551 (5th Cir.2007).
A post-judgment amendment is permissible only when the judgment is vacated pursuant to Federal Rule of Civil Procedure 59 or 60. Vielma v. Eureka Co., 218 F.3d 458, 468 (5th Cir.2000). "While Fed.R.Civ.P. 15(a) endows a district court with `virtually unlimited discretion' to allow amendments before entry of judgment, that discretion narrows considerably after entry of judgment." Id. Once the entry of judgment has occurred, it is proper to deny leave to amend "where the party seeking to amend has not clearly established that he could not reasonably have raised the new matter prior to the trial court's merits ruling." Briddle v. Scott, 63 F.3d 364, 380 (5th Cir.1995).
Benson did not request leave to amend his pleadings until after the district court entered judgment and until after the district court denied his first motion to reconsider the judgment. While he claims that the delay in presenting his new claim was caused by the Defendants' "concealment of the document that evidenced the breach of contract," the document in question was in his possession in September 2005, approximately nineteen months before he sought leave to amend on April 5, 2007. In light of Benson's delay, the district court did not abuse its discretion when it denied leave to amend.

III. CONCLUSION
For the foregoing reasons, the district court's decision is AFFIRMED.
NOTES
[1]  Eventually, on November 15, 2004, the Governance Council voted to reappoint Benson for one year, subject to a set of conditions. His new grant of privileges took effect on April 6, 2005, more than three years after St. Joseph originally decided not to renew his employment.
[2]  We note that, on rare occasions, we have permitted a Rule 60(b) motion based on a legal error to be filed after the time for filing a notice of appeal has expired. See, e.g., Lairsey v. Advance Abrasives Co., 542 F.2d 928, 930-31 (5th Cir.1976) (permitting the filing of a Rule 60(b) motion on the basis of a legal error after the time for filing a notice of appeal had expired because of a change in the law).
[3]  In evaluating an unrelated TMPA provision, the Texas Supreme Court has commented, in dicta, that "we know of no requirement that malice be proved by more than a preponderance of the evidence ... to recover actual damages." Romero v. KPH Consol., Inc., 166 S.W.3d 212, 220 (Tex.2005).
