MOORE, J., delivered the opinion of the court, in which McKEAGUE, J. and POLSTER, D. J., joined, with MOORE, J. (pp. 716 - 21), also delivering a separate concurring opinion.
OPINION
KAREN NELSON MOORE, Circuit Judge.This case involves the appeal of the district court’s dismissal pursuant to a motion for summary judgment of claims of race and sex discrimination on single- and mixed-motive theories brought by Cornelius Wright (‘Wright”), Plaintiff-Appellant, against his employer, Murray Guard, Inc. (“Murray Guard”), Defendant-Appellee, under Title VII of the Civil Rights Act of 1964, 42 U.S.C. § 2000e-2, 42 U.S.C. § 1981, and the Tennessee Human Rights Act. In addition, Wright claims that the district court erred in granting Murray Guard’s request for leave to file a reply brief on its motion for summary judgment. For the reasons explained below, we AFFIRM the district court’s judgment.
I. BACKGROUND
Wright began his work for Murray Guard as a lieutenant security guard at the *705Nike facility in Memphis, Tennessee on December 2, 2002. Wright received a company sexual-harassment policy when he started working for Murray Guard. Murray Guard’s policies, of which Wright was aware, prohibit harassment on the basis of race and sex and “sleeping with employees at Murray Guard.” Joint Appendix (“J.A.”) at 188 (Wright Dep. at 179).
On June 11, 2003, someone allowed an unauthorized person to enter the Nike facility. Three people were working at the time, including Annette Bradley, an African-American female guard whom Wright supervised. Alan Muntz, Wright’s regional manager at Murray Guard, requested that Wright investigate to determine who permitted the individual to enter the facility. Wright reported that Bradley was responsible for this breach of security. Bradley denied this, but Muntz proceeded to transfer her and told her not to have contact with anyone at Nike. On June 16, 2003, Murray Guard offered Wright a promotion to the position of captain, which Wright declined because he did not intend to stay at Murray Guard.
The Murray Guard corporate office received an anonymous letter on June 27, 2003, accusing Wright of sexually harassing and having sex with several women guards who worked at the Nike facility, including at least one Murray Guard employee. On July 3, 2003, Murray Guard told Wright about the letter. Dan Underwood, Murray Guard Vice President of Human Resources, investigated these allegations but could not confirm them. In July 2003, Wright demonstrated a number of performance problems, including failing to follow an order to staff a post with a second security officer and failing to sound the take-cover alarm according to Nike’s protocol. Nike filed a complaint about the latter incident.
Sometime in July 2003, Wright accused Bradley of spreading rumors about him. Muntz investigated and concluded that these allegations were true. Bradley’s behavior constituted a violation of Muntz’s order barring her from contacting anyone at Nike. Muntz originally intended to terminate Bradley on this ground. Muntz met with Bradley to discuss these events. Bradley told him that she was not responsible for the security breach and that Wright had harassed her and other women employees, including Jennifer Bennett, a white female guard whom Wright also supervised. Bradley’s allegations led Muntz to doubt Wright’s conclusion that Bradley was responsible for the security breach and Muntz’s decision to transfer Bradley. On this basis, Muntz changed his mind regarding terminating Bradley and instead decided to retain her and issue her a warning. Bradley then submitted incident reports detailing her allegations of sexual harassment against Wright, including incidents when Bradley had seen Wright with other female employees in situations suggesting that he had been engaging in sexual acts with them.
Based on this information, Muntz conducted a second investigation into the sexual harassment allegations against Wright, and on July 22, 2003, Muntz spoke with Bennett, who confirmed that Wright had sexually harassed her. The next day, John Reeves, a Human Resources Specialist from Murray Guard corporate headquarters, conducted an interview of Bennett. Bennett detailed Wright’s harassment of her, including pressuring her to perform oral sex on him, and explained that she feared she would lose her job if she refused to have sex with him. Bennett also named five other women employees whom Wright had sexually harassed.
On or about July 23, 2003, Wright had a meeting with Muntz and Tom Beach, Vice President of the Southern Division of Mur*706ray Guard. During this meeting, Muntz and Beach told Wright that Nike was dissatisfied with his performance and that he had been investigated for sexual harassment a second time. They then terminated Wright, explaining that this decision was based on (1) the sexual harassment allegations made against him, (2) his job performance issues, and (3) his failure to follow procedures.
Wright filed a charge with the Equal Employment Opportunity Commission (“EEOC”) claiming discrimination by Murray Guard on the basis of race and sex. On August 5, 2003, the EEOC issued Wright a right-to-sue letter. Wright filed a complaint on these grounds with the United States District Court for the Western District of Tennessee on October 22, 2003. The district court granted Murray Guard’s motion for summary judgment on each of Wright’s claims, and Wright timely filed this appeal.
II. TITLE VII CLAIMS
A. Standard of Review
We review de novo a district court’s order granting summary judgment. Di-Carlo v. Potter, 358 F.3d 408, 414 (6th Cir.2004). We will affirm a grant of summary judgment “if the pleadings, depositions, answers to interrogatories, and admissions on file, together with the affidavits, if any, show that there is no genuine issue as to any material fact and that the moving party is entitled to a judgment as a matter of law.” FED. R. CIV. P. 56(c). Summary judgment is inappropriate when the evidence raises a genuine issue about a material fact, “that is, if the evidence is such that a reasonable jury could return a verdict for the nonmoving party.” Anderson v. Liberty Lobby, Inc., 477 U.S. 242, 248, 106 S.Ct. 2505, 91 L.Ed.2d 202 (1986).
The moving party bears the burden of demonstrating that there are no genuine issues of material fact, which “may be discharged by ‘showing’' — that is, pointing out to the district court — that there is an absence of evidence to support the non-moving party’s case.” Celotex Corp. v. Catrett, 477 U.S. 317, 322-23, 325, 106 S.Ct. 2548, 91 L.Ed.2d 265 (1986). To defeat summary judgment, the nonmoving party must then put forth “significant[ ] probative” evidence in support of its position. Anderson, 477 U.S. at 249-50, 106 S.Ct. 2505. In reviewing the district court’s decision to grant summary judgment, we must view all evidence in the light most favorable to the nonmoving party. Matsushita Elec. Indus. Co. v. Zenith Radio Corp., 475 U.S. 574, 587, 106 S.Ct. 1348, 89 L.Ed.2d 538 (1986).
B. Single-Motive Claims
Title VII single-motive claims proceeding on circumstantial evidence are analyzed under the burden-shifting framework set forth in McDonnell Douglas Corp. v. Green, 411 U.S. 792, 802, 93 S.Ct. 1817, 36 L.Ed.2d 668 (1973), and later modified by Texas Department of Community Affairs v. Burdine, 450 U.S. 248, 252-53, 101 S.Ct. 1089, 67 L.Ed.2d 207 (1981). This framework first requires that the plaintiff establish a prima facie case. DiCarlo, 358 F.3d at 414. Once a prima facie case has been shown, the plaintiff is entitled to a presumption that the defendant discriminated against him or her in violation of Title VII. Id. at 414 (citing Burdine, 450 U.S. at 254, 101 S.Ct. 1089). The defendant then bears the burden of production to put forth a “legitimate, nondiscriminatory reason” for the complained of adverse treatment. Id. (citing Burdine, 450 U.S. at 253, 101 S.Ct. 1089). “The explanation provided must be legally sufficient to justify a judgment for the defendant.” Burdine, 450 U.S. at 255, 101 S.Ct. 1089. If the defendant meets this burden, the presumption of discrimination created by the prima facie case falls *707away, id. at 255, 101 S.Ct. 1089 & n. 10, and the plaintiff then needs to show that the defendant’s “ ‘legitimate nondiscriminatory reason’ ” was a “ ‘pretext for discrimination.’ ” DiCarlo, 358 F.3d at 414-15 (quoting Burdine, 450 U.S. at 253, 101 S.Ct. 1089). Throughout this burden-shifting approach, the plaintiff continues to bear the ultimate burden of proving, by a preponderance of the evidence, the intent to discriminate. St. Mary’s Honor Ctr. v. Hicks, 509 U.S. 502, 511, 113 S.Ct. 2742, 125 L.Ed.2d 407 (1993).
1. Race-Discrimination Claim
a.Prima Facie Case
To demonstrate a prima facie case, the plaintiff must show that “(1) he or she was a member of a protected class; (2) he or she suffered an adverse employment action; (3) he or she was qualified for the position; and (4) he or she was replaced by someone outside the protected class or was treated differently than similarly-situated, non-protected employees.” DiCarlo, 358 F.3d at 415. It is undisputed that Wright meets the first three elements of the prima facie case: he is African-American; he was terminated; and he was qualified for the position he held. According to Murray Guard’s memorandum in support of its motion for summary judgment, Wright responded to Murray Guard’s interrogatories that he was replaced by a white man. Although Murray Guard claims that this statement is “con-clusory, self-serving, [and] hearsay,” Appellee Br. at 16 n. 4, Murray Guard does not deny this fact, has submitted no evidence to refute it, and has made no statements regarding Wright’s replacement. Because this court must view all evidence in the light most favorable to the nonmov-ing party, Wright’s assertion regarding his replacement suffices to sustain a prima facie case.
b.Legitimate, Nondiscriminatory Reason
Murray Guard’s claimed nondiscriminatory reasons for terminating Wright’s employment are threefold: the sexual harassment allegations against Wright, Wright’s job performance issues, and Wright’s failure to follow procedures. In addition to the alleged sexual harassment, Wright ignored, from July 7 through July 11 of 2003, a direct order to staff a post with an additional security officer, and he failed, on July 22, 2003, to follow the proper procedure for sounding the take-cover alarm.1 These constitute legitimate, nondiscriminatory reasons for Wright’s termination because they are reasons, supported by admissible evidence, “which, if believed by the trier of fact, would support a finding that unlawful discrimination was not the cause of the employment action.” Hicks, 509 U.S. at 507, 113 S.Ct. 2742 (citing Burdine, 450 U.S. at 254-55, 101 S.Ct. 1089 & n. 8).
c.Pretext
“Pretext may be shown ‘either directly by persuading the [trier of fact] that a discriminatory reason more likely motivated the employer or indirectly by showing that the employer’s proffered explanation is unworthy of credence.’ ” Manzer v. Diamond Shamrock Chems. Co., 29 F.3d 1078, 1082 (6th Cir.1994) (quoting Burdine, 450 U.S. at 256, 101 S.Ct. 1089). Under the “honest belief’ rule developed by the Seventh Circuit, “so long as the employer honestly believed in the proffered reason,” an employee cannot *708prove pretext even if the employer’s reason in the end is shown to be “mistaken, foolish, trivial, or baseless.” Smith v. Chrysler Corp., 155 F.3d 799, 806 (6th Cir.1998) (citing, inter alia, Kariotis v. Navistar Int'l Trans. Corp., 131 F.3d 672, 676 (7th Cir.1997)). We have rejected the Seventh Circuit’s bare “honest belief’ doctrine and instead have adopted a modified honest-belief approach. Id. (holding that “[t]o the extent the Seventh Circuit’s application of the ‘honest belief rule credits an employer’s belief without requiring that it be reasonably based on particularized facts rather than on ignorance and mythology, we reject its approach”). Under this approach, for an employer to avoid a finding that its claimed nondiscriminatory reason was pretextual, “the employer must be able to establish its reasonable reliance on the particularized facts that were before it at the time the decision was made.” Id. at 806-07 (defining standard in the context of an Americans with Disabilities Act claim); see also Balmer v. HCA, Inc., 423 F.3d 606, 614 (6th Cir.2005) (applying Smith rule in Title VII retaliation case). Even when the employer makes such a showing, “the protection afforded by the rule is not automatic.... [Ojnee the employer is able to point to the particularized facts that motivated its decision, the employee has the opportunity to produce ‘proof to the contrary.’ ” Smith, 155 F.3d at 807 (quoting Pesterfield v. TVA, 941 F.2d 437, 443 (6th Cir.1991)).
In determining whether an employer “reasonably relied on the particularized facts then before it, we do not require that the decisional process used by the employer be optimal or that it left no stone unturned. Rather, the key inquiry is whether the employer made a reasonably informed and considered decision before taking an adverse employment action.” Id. (citing Burdine, 450 U.S. at 256, 101 S.Ct. 1089). Although we will not “miero-manage the process used by employers in making their employment decisions,” we also will not “blindly assume that an employer’s description of its reasons is honest.” Id. Therefore, “[w]hen the employee is able to produce sufficient evidence to establish that the employer failed to make a reasonably informed and considered decision before taking its adverse employment action, thereby making its decisional process ‘unworthy of credence,’ then any reliance placed by the employer in such a process cannot be said to be honestly held.” Id. at 807-08.
Murray Guard has offered evidence that it “reasonably relied on the particularized facts then before it.” Id. at 807. The facts before Murray Guard were: (a) Wright’s performance problems; (b) an anonymous letter alleging that Wright sexually harassed several women employees; (c) Bradley’s allegations, supported by incident reports, that Wright sexually harassed her, Bennett, and other women employees; and (d) Bennett’s allegation that Wright touched her in a sexual manner and pressured her into performing oral sex on him at the Nike facility and that she felt that her job would be in jeopardy if she did not have sex with him.
Although Wright argues that Murray Guard’s decision was made without sufficient investigation, the evidence belies this assertion. After receipt of the anonymous letter, Underwood conducted Murray Guard’s first investigation of the sexual harassment allegations against Wright but could not confirm these allegations. After Bradley made additional allegations regarding Wright’s having sex with other female employees, including Bennett, and filed incident reports to this effect, Murray Guard conducted another investigation.2 *709Muntz then interviewed Bennett, who talked to him about the allegations that Bradley had made. Based on this information, Muntz asked Reeves to become involved, and Reeves interviewed Bennett as well. The information regarding Wright’s performance problems came through normal channels of supervision, including Muntz and Philmore Epps, a Nike Safety Manager. Beach, who made the decision to terminate Wright, based his decision on the results of the Bennett interview, which were relayed to him by Reeves, and on Wright’s performance problems, which were relayed to him by Muntz. These procedures sufficed for Murray Guard to make a “reasonably informed and considered decision” before terminating Wright. See Smith, 155 F.3d at 807.
Wright has offered no evidence to indicate that Murray Guard made its decision on grounds other than those offered. Although Wright contends that Bradley had a motive to lie, this unsupported contention does not create a question of fact regarding Murray Guard’s assertion that it honestly believed that Wright had sexually harassed its employees. Murray Guard need not prove that Wright actually sexually harassed anyone to defeat Wright’s claims. Rather, Murray Guard needs to show that it made its decision to terminate Wright based on an honestly held belief in a nondiscriminatory reason supported by particularized facts after a reasonably thorough investigation. Murray Guard has sustained this burden. Wright has offered no evidence to the contrary, and thus he has not met his burden of proving pretext. Therefore, we affirm the district court’s dismissal of this claim.
2. Sex-Discrimination Claim
On his sex-discrimination claim, Wright has established the first three elements of the prima facie case — that he is member of a protected class, that he suffered an adverse employment action, and that he was qualified for the position — but he has failed to establish the fourth element. See DiCarlo, 358 F.3d at 415. Plaintiff was replaced by a male, and he has not shown that he “was treated differently than similarly-situated non-protected employees.” See id.
Wright claims that he was treated differently than women with regard to the disciplinary process at Murray Guard. Wright’s only proposed example of a similarly situated female employee is Annette Bradley. Wright claims that Bradley was afforded an opportunity to refute the allegations made against her that were to lead to her discharge, and that Murray Guard then changed its decision to terminate her, whereas Wright was not given the same opportunity to rebut the sexual harassment allegations made against him that ultimately led to his discharge. Wright also complains that Murray Guard reopened the investigation of the sexual harassment allegations made against him based on the statements of Bradley, who had admitted to spreading rumors about Wright, without proof of who was telling the truth.
Taking all of his allegations as true, we conclude that Wright has failed to make out a prima facie case of sex discrimination because he has not shown that he and Bradley were similarly situated. “The plaintiff need not demonstrate an exact correlation with the employee receiving *710more favorable treatment in order for the two to be considered ‘similarly-situated.’ ” Ercegovich v. Goodyear Tire & Rubber Co., 154 F.3d 344, 352 (6th Cir.1998) (considering claim under the Age Discrimination in Employment Act). As the Supreme Court recently held in the context of a claim of race-based peremptory strikes of jurors, “a rule that no comparison [among prospective jurors] is probative unless the situation of the individuals compared is identical in all respects” would make claims of discrimination “inoperable,” because “potential jurors are not products of a set of cookie cutters.” Miller-El v. Dretke, 545 U.S. 231, - n. 6, 125 S.Ct. 2317, 2329 n. 6, 162 L.Ed.2d 196 (2005). This reasoning applies with equal force to the employment-discrimination context. Therefore, to establish that an employee is an appropriate comparator, “the plaintiff [must] demonstrate that he or she is similarly situated to the [claimed comparator] in all relevant respects.” Ercegovich, 154 F.3d at 353.
In the disciplinary context, we have held that to be found similarly situated, the plaintiff and his proposed comparator must have engaged in acts of “comparable seriousness.” Clayton v. Meijer, Inc., 281 F.3d 605, 611 (6th Cir. 2002) (applying the Ercegovich approach to a Title VII claim) (quoting McDonald v. Santa Fe Transp. Co., 427 U.S. 273, 283 n. 11, 96 S.Ct. 2574, 49 L.Ed.2d 493 (1976)). To make this assessment, we may look to certain factors, such as whether the individuals “ ‘have dealt with the same supervisor, have been subject to the same standards and have engaged in the same conduct without such differentiating or mitigating circumstances that would distinguish their conduct or the employer’s treatment of them for it.’ ” Ercegovich, 154 F.3d at 352 (quoting Mitchell v. Toledo Hosp., 964 F.2d 577, 583 (6th Cir.1992)). However, when such factors are not relevant, we need not consider them. Id. Rather, to determine whether two individuals are similarly situated with regard to discipline, we “make an independent determination as to the relevancy of a particular aspect of the plaintiffs employment status and that of the [proposed comparable] employee.” Id.
Wright cannot be considered similarly situated to Bradley for the purposes of discipline because they engaged in different conduct, and the differences in their conduct are relevant. Bradley allegedly failed to follow a procedure by allowing an unauthorized person into the Nike facility and allegedly spread rumors about Wright, which violated an order that she not have contact with anyone at Nike.3 Wright allegedly sexually harassed at least one of his subordinates, including coercing one or more into having sexual relations with him. As a result of these distinct alleged instances of misconduct, Bradley was transferred to another facility after she supposedly did not follow the security procedure, and Wright was ultimately terminated.
Wright and Bradley are not similarly situated because their alleged acts of misconduct are of a very different nature, and there are legitimate reasons why Murray Guard would treat them differently. First, Wright’s alleged misconduct, which, if true, would constitute a serious violation of federal law, would be much more likely to expose Murray Guard to liability than Bradley’s alleged misconduct. Murray *711Guard is permitted to consider its legal obligations, especially to a class of people protected by federal and state law that is made vulnerable by a particular employee’s alleged misconduct, in its disciplinary decisions regarding its employees. Second, Wright’s alleged misconduct, if true, caused actual serious harm to the people with whom he interacted, whereas Bradley’s alleged misconduct, if true, at most caused Wright some secondary harm through the effect of the rumors. Cf. Clayton, 281 F.3d at 611-12 (holding that plaintiff and another employee were not similarly situated when they engaged in the same conduct but plaintiff caused serious injury and other employee did not). Finally, Bradley’s alleged misconduct could be susceptible to correction with a warning, and, if corrected, would have no further consequences on the experience of those around her as she was no longer working at Nike. By contrast, the nature of Wright’s alleged misconduct, even were it to cease, would make it challenging for him to continue successfully in his position because it would be difficult for those he had harassed (and perhaps others) to work with him. Therefore, we affirm the district court’s judgment that Wright failed to present a prima facie case of sex discrimination.
C. Mixed-Motive Claims
1. The 1991 Civil Rights Act and Desert Palace
Individual disparate-treatment claims brought pursuant to Title VII of the Civil Rights Act of 1964 (“Title VII”), 42 U.S.C. § 2000e-2, are often categorized as either single-motive claims, i.e., when an illegitimate reason motivated an employment decision, or mixed-motive claims, when “both legitimate and illegitimate reasons motivated the decision,” Desert Palace v. Costa, 539 U.S. 90, 93, 123 S.Ct. 2148, 156 L.Ed.2d 84 (2003). The Supreme Court first recognized the mixed-motive theory in Price Waterhouse v. Hopkins, where the Court held, in a plurality opinion, that a plaintiff could shift the burden of proof to the employer to prove an affirmative defense upon a showing that the protected characteristic “‘played a motivating part in an employment decision.’ ” Desert Palace, 539 U.S. at 93, 123 S.Ct. 2148 (quoting Price Waterhouse v. Hopkins, 490 U.S. 228, 258, 109 S.Ct. 1775, 104 L.Ed.2d 268 (1989) (plurality opinion)). The employer would then be held liable unless it “ ‘prov[ed] by a preponderance of the evidence that it would have made the same decision even if it had not taken plaintiffs [protected trait] into account.’ ” Id. (quoting Price Waterhouse, 490 U.S. at 258, 109 S.Ct. 1775).
Then, in an attempt “ ‘to eliminate the employer’s ability to escape liability in Title VII mixed-motive cases by proving that it would have made the same decision in the absence of the discriminatory motivation,’ ” Rachid v. Jack In The Box, Inc., 376 F.3d 305, 312 n. 8 (5th Cir.2004) (quoting Hill v. Lockheed Martin Logistics Mgmt., Inc., 354 F.3d 277, 284 (4th Cir.2004)), Congress enacted the 1991 Civil Rights Act (“the 1991 Act”), which amended Title VII, Pub.L. No. 102-166, § 107, 105 Stat. 1071, 1075-76 (1991) (codified at 42 U.S.C. §§ 2000e-2(m) and 2000e-5(g)(2)(B)). One of the new statutory provisions codified the mixed-motive “alternative for proving that an ‘unlawful employment practice’ has occurred.” Desert Palace, 539 U.S. at 94, 123 S.Ct. 2148 (quoting 42 U.S.C. § 2000e-2(m)). The provision states that a plaintiff can raise a mixed-motive Title VII claim by “demons-tratfing] that race, color, religion, sex, or national origin was a motivating factor for any employment practice, even though other factors also motivated the practice.” 42 U.S.C. § 2000e-2(m) (emphasis added). If the plaintiff makes such a showing, she *712is entitled to relief. However, the 1991 Act also provides that the employer’s liability will be limited to injunctive and declaratory relief and attorney fees and costs if the employer can establish that it “would have taken the same action in the absence of the impermissible motivating factor.” Id. § 2000e-5(g)(2)(B). The declaratory and injunctive relief may not include “an order requiring any admission, reinstatement, hiring, promotion, or payment.” Id. § 2000e-5(g)(2)(B)(ii).
After Price Waterhouse, despite Congress’s attempt to clarify the standard to prove a mixed-motive claim, the question lingered as to whether direct evidence was required to establish a mixed-motive claim. We held that direct evidence of discrimination was required to present a mixed-motive claim. Gagne v. Northwestern Nat'l Ins. Co., 881 F.2d 309, 315 (6th Cir.1989). This more stringent requirement for presenting a mixed-motive claim kept such claims distinct from claims analyzed under the McDonnell Douglas framework, which was applied when the plaintiff relied on circumstantial evidence. Then, in 2003, the Supreme Court unanimously interpreted the 1991 Civil Rights Act to allow plaintiffs to bring mixed-motive discrimination claims based solely on circumstantial evidence, Desert Palace, 539 U.S. at 101-02, 123 S.Ct. 2148, thereby overruling our decision in Gagne.
Prior to Desert Palace, we did not require a plaintiff to present a prima facie case or follow the McDonnell Douglas burden-shifting framework to get to the jury on a mixed-motive claim. See, e.g., Cesaro v. Lakeville Cmty. Sch. Dist., 953 F.2d 252, 254 (6th Cir.1992). Rather, the employee only needed to show that the illegitimate reason “was a motivating factor in an employment decision,” and then “the employer [could] avoid liability only by proving by a preponderance of the evidence that it would have made the same decision even if it had not considered the plaintiffs gender.” Id. However, now that such mixed-motive claims can be brought based on circumstantial evidence, the question arises as to the effect of Desert Palace on the analysis of mixed-motive claims at the summary judgment stage.4 What is clear from Desert Palace, regardless of its impact on the McDonnell Douglas framework, is that to succeed on a mixed-motive claim, the plaintiff must adduce evidence that the protected charac*713teristic “was a motivating factor” in the employer’s adverse employment decision. 42 U.S.C. § 2000e-2(m) (emphasis added). “The ultimate question in every employment discrimination case involving a claim of disparate treatment is whether the plaintiff was a victim of intentional discrimination.” Reeves, 530 U.S. at 153, 120 S.Ct. 2097. Applying Desert Palace and the 1991 Act to this standard, the ultimate question at summary judgment on a mixed-motive case is “whether the plaintiff has presented evidence, direct or circumstantial, from which a reasonable jury could logically infer that [a protected characteristic] was a motivating factor in [the defendant’s adverse employment action against the plaintiff].” Harris v. Giant Eagle, Inc., 133 Fed.Appx. 288, 297 (6th Cir.2005) (unpublished opinion) (alteration in original) (internal quotation marks omitted); accord 42 U.S.C. § 2000e-2(m); Stegall v. Citadel Broad. Co., 350 F.3d 1061, 1068 (9th Cir.2003).
2. Application
Wright cannot overcome Murray Guard’s motion for summary judgment on his mixed-motive claim because he has not offered sufficient evidence, direct or circumstantial, to create a genuine issue of material fact on whether his race or sex “ “was a motivating factor’ ” in Murray Guard’s decision to terminate him. Desert Palace, 539 U.S. at 94, 123 S.Ct. 2148 (quoting 42 U.S.C. § 2000e-2(m)). Many of Wright’s arguments in support of his mixed-motive claims are conclusory allegations unsupported by any evidence and thus cannot create a genuine issue of material fact.5 The specific evidence that Wright cites to support his argument that Murray Guard’s decision was tainted by an unlawful motive similarly does not suffice to create a genuine issue of material fact on this question. Wright claims that his different treatment in the disciplinary process, especially that he was not given a chance to refute allegations whereas Bradley was, supports the conclusion that Murray Guard considered an unlawful motive. However, the different treatment of Wright and Bradley does not bear this inference because the alleged acts of misconduct so diverged that they merited different treatment, as explained above.
Wright also makes unsupported claims that various aspects of Murray Guard’s investigation of the sexual harassment allegations made against him evince a discriminatory motive. Wright’s assertion that there was a second sexual harassment investigation based on the same facts is unfounded; Murray Guard reopened the investigation based on new allegations made against Wright. That Beach did no investigation is irrelevant because he made his decision based on the investigations of others. Wright’s criticisms of the rigor of Murray Guard’s investigation do not create an issue of fact regarding the company’s motives because the investigation was sufficiently thorough to foreclose the conclusion that it was insincere. That Murray Guard decided to credit the statements of Bradley, who Wright claims spread rumors and had a motive to lie, and the statements of Bennett, who Wright claims was acting defensively to prevent her own discharge, was within the company’s discretion and does not create an issue of fact as to whether Murray Guard considered race or sex in its decision to terminate Wright.
*714Wright also makes the unfounded assertions that there was no documentation of his poor performance and that the company’s offer of a promotion to him undermines Murray Guard’s proffered reason for his discharge. The record shows that Wright failed to follow both company protocol and his supervisor’s orders, and that the offer of promotion was made prior to these performance problems.6
To defeat Murray Guard’s motion for summary judgment on his mixed-motive claim, Wright must “demonstrate[ ]” that his race or sex “was a motivating factor” in Murray Guard’s decision to terminate him, 42 U.S.C. § 2000e-2(m), and that he has failed to do.7 At most, Wright has presented evidence as to why the allegations of sexual harassment made against him might not be credible, but he has presented no evidence that Murray Guard did not honestly believe they were true or that Murray Guard relied on unlawful motives in terminating Wright. Because Wright has not established a genuine issue of material fact as to whether an unlawful factor motivated his termination, the district court properly dismissed his mixed-motive claim.
III. CLAIMS UNDER 42 U.S.C. § 1981 AND THE TENNESSEE HUMAN RIGHTS ACT8
We also affirm the district court’s grant of summary judgment on Wright’s claims under both 42 U.S.C. § 1981 and the Tennessee Human Rights Act (“THRA”). Because Wright’s Title VII claims for race and sex discrimination fail, his claims for race and sex discrimination on the same grounds fail under these statutes as well. See Noble v. Brinker Int’l, Inc., 391 F.3d 715, 720 (6th Cir.2004) (§ 1981); Newman v. Fed. Express Corp., 266 F.3d 401, 406 (6th Cir.2001) (THRA).
IV. REPLY BRIEF
A. Standard of Review
The decision to grant a motion for leave to file a reply brief relies on the interpretation and application of local rules and local practice. As these are matters within the district court’s discretion, the district court’s decision is reviewed for abuse of discretion. See generally 1 STEVEN ALAN CHILDRESS & MARTHA S. DAVIS, FEDERAL STANDARDS OF REVIEW §§ 4.01, 4.10, 4.11 (3d ed.1999).
B. The District Court Did Not Abuse Its Discretion
Although the Federal Rules of Civil Procedure do not specifically authorize the filing of reply briefs, they likewise do not prohibit it. See FED. R. CIV. P. 56. The Western District of Tennessee Model Scheduling Order for Routine Cases states that
Neither party may file [a] ... reply ... without leave of the court. If a party believes that a reply is necessary, it *715shall file a motion for leave to file a reply accompanied by a memorandum setting forth the reasons for which a reply is required.
J.A. at 43 (W. Dist. of Tenn. Model Sched. Order for Routine Cases at 3).
According to the district court’s docket sheet, on January 10, 2005, Murray Guard filed a motion for leave to file a reply brief. The docket sheet indicates that Wright never filed an objection to the motion. The district court granted the motion on January 11, 2005 and entered Murray Guard’s reply brief on that same date.9 On January 21, 2005, Wright filed a response to Murray Guard’s reply. In his response, Wright addressed the merits of Murray Guard’s reply, but did not object to the order granting Murray Guard permission to file the reply brief.
Because Wright made no objection below to the district court’s decision to allow the reply brief, he forfeited this objection and cannot raise it in the first instance in this court.10 Even if this panel were to consider the merits of Wright’s claim, it would fail. Wright offers no reason why the district court abused its discretion in this ruling other than his faulty assertion that the district court was not empowered to grant this motion.11 Although the scheduling order requires the filing of a memorandum stating reasons in support of a motion for leave to file a reply brief, the court’s order states that it granted Murray Guard’s motion “[fjor good cause shown.” J.A. at 341 (Order Granting Def. Murray Guard Inc.’s Mot. for Leave to File Reply Br. in Supp. of Its Mot. for Summ. J.). This is supported by the circumstances. In its reply brief, Murray Guard raised issues — that Wright’s response did not comply with local rules, that Wright’s affidavit, which accompanied his response, contradicted his deposition testimony, and that Wright raised a claim of sex discrimination for the first time in his response — that could not have been raised before seeing Wright’s response brief. Significantly, we note that Wright himself was permitted to respond via a sur-reply to the now-challenged reply by Murray Guard. In view of all the circumstances, the district court acted well within its discretion.
V. CONCLUSION
For the foregoing reasons, we AFFIRM the district court’s judgment.
. Wright argues that Murray Guard’s offer to promote him evidences that these issues with his job performance, are mere pretext. However, the offer of promotion was made to Wright on June 16, 2003, before these performance issues arose and before Murray Guard received the anonymous letter containing allegations of Wright’s sexual harassment.
. Wright argues that Underwood’s inability to confirm the initial sexual harassment allegations against him and Murray Guard's second *709investigation undermine Murray Guard's honestly held belief. However, the second investigation was conducted after new evidence— Bradley's allegations — was presented to Murray Guard for the first time, and thus an additional investigation based on these new allegations was entirely appropriate.
. In claiming that he and Bradley are similarly situated in terms of discipline, Wright is not clear to which of Bradley's infractions he is referring — allowing the unauthorized person into the facility or spreading rumors. This is immaterial, however, as neither alleged instance of misconduct is of "comparable seriousness” to Wright’s alleged misconduct. See Clayton, 281 F.3d at 611.
. Two of our prior decisions have addressed the issue of mixed-motive jury instructions after the Desert Palace decision. See Barnes v. City of Cincinnati, 401 F.3d 729, 740 (6th Cir.2005); Gibson v. City of Louisville, 336 F.3d 511, 512-14 (6th Cir.2003). Two unpublished opinions have addressed the interaction of Desert Palace and the McDonnell Douglas burden-shifting framework, but neither discussed the issue at length. See Aquino v. Honda of Am., Inc., 158 Fed.Appx. 667, 675-76 (6th Cir.2005) (unpublished opinion) (suggesting that Desert Palace incorporated the mixed-motive analysis into the McDonnell Douglas framework as applied in a Title VII claim, by explaining that after a prima facie case has been shown and the employer has presented a legitimate, nondiscriminatory reason for its decision, the employee can proceed to trial by demonstrating that an illegitimate reason was a motivating factor in the decision rather than by proving pretext, but holding that Desert Palace does not modify McDonnell Douglas as applied to claims under 42 U.S.C. § 1981); Harris v. Giant Eagle, Inc., 133 Fed.Appx. 288, 297 (6th Cir.2005) (unpublished opinion) (expressly declining to resolve interaction issue and instead focusing on the "crucial question” of whether an illegitimate reason was a motivating factor in the employment decision). As detailed in the concurring opinion, our sister circuits have employed a variety of approaches in discerning the impact of Desen Palace. Because, however, for the reasons set forth below, the facts of the instant case do not require resolution of the question, we refrain today from announcing a new or modified framework for evaluation of mixed-motive claims at the summary judgment stage.
. For instance, Wright asserts that the "fact finder might infer the use of an improper motive,” Appellant Br. at 16; that "[r]easonable minds could differ as to ... whether ... the 'honest belief defense is true,” id..; that "common sense ... suggests] that discrimination has occurred,” id. at 21; and that "[t]he Defendant’s explanation ... of ‘honest belief’ is not credible,” id. at 29.
.Wright also makes several claims that are irrelevant to whether Murray Guard's decision was prompted, at least in part, by an unlawful motive. That Wright denied the allegations of sexual harassment in his affidavit is irrelevant to the question of whether an unlawful motive played a role in the decision to terminate him. The assertion that Nike was not dissatisfied with Wright's performance is not supported by the record, and, in any event, is immaterial if Murray Guard, his employer, was not satisfied.
. In fact, Wright appears to admit that Murray Guard's decision was not based on an unlawful motivation by stating that his termination was a "pre-emptive firing": "[a] discharge because of the alleged fear of litigation.” Appellant Br. at 18, 25.
. Wright additionally brought claims under 42 U.S.C. §§ 1983 and 1985, both of which the district court dismissed. Because Wright does not mention § 1983 or § 1985 to this court, he has abandoned his appeal on these grounds.
.The docket sheet does not indicate that Murray Guard filed a memorandum in support of its motion, nor can one be located. However, the order granting Murray Guard's motion to file a reply brief states that “[t]he Clerk shall file the Reply Brief which has been lodged with the Clerk.” J.A. at 341 (Order Granting Def. Murray Guard Inc.'s Mot. for Leave to File Reply Br. in Supp. of Its Mot. for Summ. J.). The docket sheet also states that Murray Guard’s motion for leave to file the reply brief was filed on January 10, 2005 and was entered on January 11, 2005. Therefore, it is possible that Murray Guard filed its reply brief with its motion, and that the reply brief would suffice as "a memorandum setting forth the reasons for which a reply is required,” J.A. at 43 (W. Dist. of Tenn. Model Sched. Order for Routine Cases at 3), because the brief discusses several reasons why the reply was necessary. Neither party has attempted to explain these details regarding the filing of documents related to the reply brief. These facts, though potentially elucidating, are immaterial, because, as we explain in the text, the district court did not abuse its discretion by granting the motion even if Murray Guard had not filed its reply brief or some other document supporting its motion for leave to file a reply.
. Although only one day passed between the filing of the motion and the district court granting it, leaving Wright with little time to object, he could have objected in his sur-reply brief, but did not do so.
. Wright did not mention that Murray Guard did not file a memorandum in support of its motion.