
521 F.3d 765 (2008)
Cornelious WILLIAMS, Plaintiff-Appellant,
v.
AIRBORNE EXPRESS, INC., Defendant-Appellee.
No. 07-2225.
United States Court of Appeals, Seventh Circuit.
Argued March 4, 2008.
Decided April 8, 2008.
*766 Danny L. Windham (argued), Childers & Windham, Chicago, IL, for Plaintiff-Appellant.
Jody A. Ballmer (argued), Littler Mendelson, Chicago, IL, for Defendant-Appellee.
Before CUDAHY, KANNE, and EVANS, Circuit Judges.
KANNE, Circuit Judge.
Cornelious Williams was fired from his job as a driver for Airborne Express. He sued Airborne, claiming he was fired because he is African-American, in violation of Title VII of the Civil Rights Act of 1964. See 42 U.S.C. § 2000e-2. The district court granted summary judgment for Airborne. The court reasoned that Williams could not prove that any similarly situated employee had been treated differently or that Airborne's reason for firing him was a pretext for discrimination. We affirm.
Williams admitted most of the relevant facts in his response to Airborne's statement of undisputed facts. In his appellate briefs he now tries to contradict some of what he admitted at summary judgment, but he is bound by his admissions. See Holmes v. Village of Hoffman Estates, 511 F.3d 673, 680-81 (7th Cir. 2007). So, we set forth the facts as agreed by the parties and note where there remains a dispute.
Williams worked at Airborne for approximately nine years. He was a member of the International Brotherhood of Teamsters, AFL-CIO, Local No. 705, which is party to a collective bargaining agreement with Airborne. He was a union steward from 1999 until Airborne fired him.
It seems to be Airborne's practice to "terminate" employees who violate Airborne's policies, and then later to investigate their conduct and determine whether a lesser punishment is appropriate. Williams was no stranger to this procedure. In March 2002 he was terminated for exercising in a gym in the Sears Tower instead of making his scheduled deliveries. Mark Simpson, the District Field Service Manager, investigated the incident and decided to reinstate Williams after he served a suspension. In August 2002 Williams was terminated for gross insubordination after he screamed at a supervisor and called him a coward, and again Simpson reduced the punishment to a suspension. *767 Williams's personnel records also show that in 1998 he was "taken out of service" for gross insubordination.
But the last straw, according to Airborne, was a heated argument that Williams had with Eric Stiverson, a field supervisor. In January 2003 Williams saw Stiverson handling freight. Williams believed Stiverson was violating the terms of the collective bargaining agreement because, under the agreement, members of management generally are not allowed to handle freight. Williams expressed his concern to Stiverson, and Stiverson replied that he was conducting a security audit that did not violate the agreement. Williams was unsatisfied with Stiverson's response, so he and Andre Polk, another union steward, went into Airborne's office to file a grievance. Stiverson followed Williams into the office. The situation quickly escalated and became heated. Stan Foster, another union steward, testified at his deposition that the ensuing argument was the worst he had ever seen. Williams alleged that Stiverson was the aggressor, and testified at his own deposition that Stiverson pushed "up against [his] back." Stiverson asked Williams his name  Stiverson and Williams generally did not work during the same shift  and whether he was "on the clock." Williams would not answer the questions and shouted, "You know who I am." Stiverson then terminated Williams on the spot and demanded his Airborne identification card. Williams responded by extending his arms and screaming repeatedly, "If you're so hard, come and take it." Stiverson thought Williams was challenging him to a fight. Michael Montgomery, a manager, also asked Williams to hand over his identification, to no avail. Williams eventually left with his identification. Stiverson and Montgomery sent memos to Williams telling him that he had been terminated for gross insubordination and failure to turn over company property.
Although Stiverson and Montgomery were authorized to terminate employees, Simpson reviewed their decisions and had the discretion to uphold or modify the punishments. Simpson investigated the confrontation between Williams and Stiverson and reviewed the decision to terminate Williams. Simpson interviewed witnesses and concluded that Williams had ignored Stiverson's and Montgomery's requests, and that Stiverson believed Williams was trying to start a fight. Simpson also learned that customers at the front counter had overheard the argument. He concurred that Williams had been insubordinate and had failed to turn over company property. Simpson approved the discharge of Williams based on the findings of his investigation and Williams's prior disciplinary problems.
The union filed a grievance on behalf of Williams. The union and Airborne presented evidence at a hearing before a board comprised of six representatives designated by the union and management, and the board upheld Airborne's decision to fire Williams.
Williams lodged a charge of discrimination with the Equal Employment Opportunity Commission and received a right-to-sue letter. He then filed suit in district court. The parties took discovery, and Airborne moved for summary judgment. The district court granted Airborne's motion, reasoning that Williams lacked evidence that any similarly situated employee who is not African-American had been treated differently and, alternatively, that Williams could not establish that Airborne's stated reason for filing him was a pretext for discrimination.
De novo review, see Gates v. Caterpillar, Inc., 513 F.3d 680, 685 (7th Cir.2008), shows that the district court properly granted summary judgment in favor of Airborne. Williams did not offer direct *768 evidence of discrimination, nor did he introduce enough evidence to survive summary judgment under the indirect method. See McDonnell Douglas Corp. v. Green, 411 U.S. 792, 802, 93 S.Ct. 1817, 36 L.Ed.2d 668 (1973); Anders v. Waste Mgmt. of Wis., Inc., 463 F.3d 670, 676 (7th Cir.2006).
Williams did not establish a prima facie case. Airborne already had disciplined him three times (twice in the previous year) and still he was insubordinate again, so he could not show that he was meeting Airborne's legitimate job expectations. See Squibb v. Mem'l Med. Ctr., 497 F.3d 775, 788 (7th Cir.2007).
Moreover, Williams produced no evidence that any similarly situated white employee was treated more favorably. In the district court Williams asserted that several white employees were similarly situated, but on appeal he abandons that contention as to all but Kyle Hengsen. Williams points to Hengsen's declaration that he was terminated "at least three times for gross insubordination" and that each time Airborne "rescinded" his termination. But after discovery Williams was able to corroborate only one of these purported terminations. Hengsen once was suspended for gross insubordination because he pulled a driver off an assignment to complete a grievance form, and Simpson later reduced his punishment to a suspension. Airborne offered evidence that Hengsen was reinstated because this was his first offense, and so Williams cannot compare himself to Hengsen because Williams was reinstated after being terminated at least two times. As for the other incidents that supposedly led to Hengsen being terminated and reinstated, Williams did not supply details about these other incidents and thus could not establish that he and Hengsen engaged in similar behavior. See Gates, 513 F.3d at 690-91 (plaintiff must identify comparators who engaged in like conduct under like circumstances). Furthermore, Williams offered no evidence about how long Hengsen had worked for Airborne or how much time had passed between his incidents of insubordination, but this information is especially relevant when a plaintiff, like Williams, attempts to compare himself to another employee based on the number of reprimands each received. See Crawford v. Ind. Harbor Belt R.R. Co., 461 F.3d 844, 846 (7th Cir.2006).
The failure to establish any single element of the prima facie case dooms a discrimination claim. See Bio v. Fed. Express Corp., 424 F.3d 593, 596 (7th Cir. 2005). But even if Williams had made out a prima facie case, he did not offer evidence to show that Airborne's stated reason for firing him was a pretext for discrimination. Simpson, the ultimate decisionmaker, investigated the incident and upheld Williams's termination because Williams had been grossly insubordinate, he tried to pick a fight after he was terminated, he failed to turn over his identification, and he already had been terminated at least twice. Williams recites a bevy of reasons why he believes Airborne's stated rationale is not true, but none of them could establish that Airborne's reason was a lie. See Burks v. Wis. Dep't of Transp., 464 F.3d 744, 754 (7th Cir.2006).
Williams argues that Airborne could not have discharged him for refusing to relinquish his identification because Stiverson terminated him before demanding the identification. But this argument misapprehends Airborne's procedures. An employee is not discharged permanently as soon as he is terminated. Rather, a supervisor investigates the circumstances surrounding the termination and makes the final decision whether to discharge the employee. Simpson acted consistently with *769 this policy when he decided not to reinstate Williams in part because Williams continued his aggressive conduct and refused to turn over his identification after he was terminated for gross insubordination. Williams also insists that Airborne does not require fired employees to return their identification cards. But this assertion is belied by Williams's statement to the grievance board that he knew he was required to turn over his identification when he was discharged. Nowhere in his briefs does Williams acknowledge this prior admission. Williams also protests that gross insubordination could not have been the real reason he was discharged because, he asserts, Airborne had no written policy defining "gross insubordination," the company sanctioned white employees less severely for gross insubordination, and the company often failed to discipline other employees who argued with supervisors. We have never required proof of a written policy to show that an employer's decision was not a pretext for discrimination. And, as we already have described, Williams put forward no evidence from which we can make a valid comparison between Williams's conduct and that of white employees. The remaining reasons Williams provides either misstate or lack support in the record. Thus, Williams gives this court no reason to distrust Airborne's legitimate reason for firing him.
Accordingly, the judgment of the district court is AFFIRMED.
