OPINION
BOGGS, Chief Judge.
Elbert Nichols entered a conditional guilty plea to one count of being a felon in possession of a firearm, in violation of 18 U.S.C. §§ 922(g)(1) and 924, reserving his right to appeal the district court’s denial of his suppression motion. On appeal, he raises three arguments: (1) that the police officer’s decision to run a warrant check on him was based on his race, violating the Equal Protection Clause of the Fourteenth Amendment; (2) that the search of his vehicle incident to his arrest violated the Fourth Amendment; and (3) that the questioning by the police after his arrest violated his Fifth Amendment rights under
Miranda v. Arizona,
384 U.S. 436, 86 S.Ct. 1602, 16 L.Ed.2d 694 (1966). Finding no constitutional violations that would vitiate Nichols’s conviction, we AFFIRM the judgment of the district court.
I
In the early morning hours of September 9, 2004, Metro Nashville Police Department Officers Aaron Wigginton and Yannick Deslauriers were on patrol in the West Nashville area near Tennessee State University. Officer Wigginton “saw a vehicle that kind of grabbed [his] attention.” There were some men standing around the car who “quickly walked away” as the officer drove by. Officer Wigginton radioed to Officer Deslauriers: “I kind of alerted him that there was a vehicle up here that appeared as the people were kind of standing around it and didn’t want to hang around, they avoided me. I gave him the tag off the ear....” Responding to this radio call, Officer Deslauriers then
“ran the tag over [his] computer in the car,” which provided information from two systems — the National Crime Information Center (NCIC) and a Tennessee state system. The NCIC system responded first, and “nothing came back as suspicious,” so the officers “moved on” and continued patrolling the area for a few minutes. Officer Deslauriers passed by the location where the vehicle was parked and apparently saw the men trying to avoid him as well.
After a few minutes, the state system in Officer Deslauriers’s patrol car responded and reported that the vehicle was registered to “Elbert Nichols.” Officer Deslau-riers then “decided to run Elbert Nichols on our warrant system ... [and] it came back with having a [robbery] warrant on a male black. We had driven by the location and seen that there was two black guys in the yard next to the car.” The officers positioned themselves to watch the vehicle. After a few minutes, the car started to drive away, and the officers executed a stop by turning on their blue lights. As they approached the vehicle, they could see that the passenger was quite agitated and kept yelling at the driver to “stomp it” or “punch it.” Officer Deslauriers recognized the passenger as Elbert Nichols from the mug shot that had come up on his computer system. The driver made clear that he was not going to try to run, and Officer Deslauriers then took Nichols into custody and placed him in the back of his patrol car. Officer Deslauriers informed Nichols of his
Miranda
rights and advised him he was under arrest for the outstanding robbery warrant. Nichols stated that he understood his rights, but denied that he was Elbert Nichols, even when the officer pointed out his mug shot on the computer system.
Officer Déslauriers then proceeded to search the vehicle and discovered a loaded .38-caliber handgun in the glove box directly in front of where Nichols had been sitting. The glove box was locked, but the officer opened it with a set of keys found at the scene.
Officer Deslauriers testified that the search lasted “[a] couple minutes. Not very long.” After recovering the gun, Officer Deslauriers returned to his patrol car and confronted Nichols with it. Initially, Nichols continued to deny that he was Elbert Nichols. However, as Officer Deslauriers began to do the arrest report, and engaged Nichols in “general conversation about the paperwork,” Nichols soon dropped the charade and admitted his identity, but insisted that the robbery warrants were a mistake. In response to the district court’s inquiry regarding how long the defendant had denied his identity, Officer Deslauriers testified, “Several minutes while I spoke to him initially. Even after I searched the car. He finally admitted— I think he had a mole on his face. Finally he just got tired, I assume.” Later, as he was being transported back to the police station, Nichols “refused to be interviewed any further.”
On the basis of these facts, the district court refused to suppress any of the evidence. Regarding the alleged equal protection violation, the court held that the
defendant had failed to establish a
prima, facie
case that race was a motivating factor in the actions of the officers since the defendant’s evidence was essentially no more than “that [the officers were] white and [were] patrolling in a predominantly black neighborhood....” The court next summarily rejected Nichols’s argument that the search of a locked glove box exceeded the proper scope of a search incident to arrest, citing Seventh Circuit cases holding that such a search was permissible under prevailing Supreme Court precedent. Finally, the district court rejected Nichols.’s
Miranda
argument, concluding that the “Defendant’s repeated denials of his identity were not refusals to answer all police questions. Rather, Defendant wished to, and did, communicate affirmatively with the police officers by making statements to them which he believed furthered his self-interest.” The court therefore concluded that Nichols impliedly waived his right to remain silent.
Having failed in his motion to suppress, Nichols entered a conditional guilty plea pursuant to Federal Rule of Criminal Procedure 11(a)(2) and appealed to this court.
II
“When reviewing the denial of a motion to suppress, [this court] review[s] the district court’s findings of fact for clear error and its conclusions of law
de novo.” United States v. Foster,
376 F.3d 577, 583 (6th Cir.2004). “A factual finding will only be clearly erroneous when, although there may be evidence to support it, the reviewing court on the entire evidence is left with the definite and firm conviction that a mistake has been committed.”
United States v. Navarro-Camacho,
186 F.3d 701, 705 (6th Cir.1999). Additionally, the evidence produced at a suppression hearing must be viewed “in the light most likely to support the district court’s decision.”
Ibid.
A
Nichols first contends that Officer Deslauriers’s decision to run a warrant check on the name “Elbert Nichols” was motivated by race, claiming that Officer Deslauriers presumed Nichols to be black. Appellant’s Br. at 19-20. Nichols relies principally upon
United States v. Avery,
137 F.3d 343 (6th Cir.1997), in asserting this claim.
Avery
involved the surveillance of a young black male by narcotics officers in the Cincinnati airport based' on what they perceived to be suspicious behavior. 137 F.3d at 346. The defendant in that case was eventually discovered to be transporting illegal drugs; he moved to suppress the evidence claiming that the “officers targeted, pursued and interviewed him solely due to his race.”
Id.
at 346-47. Although the court ultimately determined that there was no equal protection violation, it elaborated on the applicable doctrine in an oft-repeated
dictum:
[W]e find that citizens are entitled to protection of the laws at all times. If law enforcement adopts a policy, employs a practice, or in a given situation takes steps to initiate an investigation of a citizen based solely upon that citizen’s race, without more, then a violation of the Equal Protection Clause has occurred.
Id.
at 355.
Avery, in turn, relied on earlier
dicta
in this court’s decision in
United States v. Travis,
62 F.3d 170, 173-74 (6th Cir.1995), where we noted that consensual encounters initiated solely on the basis of
race may violate the Equal Protection Clause. Although not binding, these cases support the view that checking individuals for outstanding warrants in an intentionally racially discriminatory manner may violate the Equal Protection Clause.
See also Whren v. United States,
517 U.S. 806, 813, 116 S.Ct. 1769, 135 L.Ed.2d 89 (1996) (noting that the Equal Protection Clause prohibits “selective enforcement of the law based on considerations such as race”).
While we, of course, agree with the general proposition that selective enforcement of the law based on a suspect’s race may violate the Fourteenth Amendment, we do not agree that the proper remedy for such violations is necessarily suppression of evidence otherwise lawfully obtained. The exclusionary rule is typically applied as a remedy for Fourth Amendment violations, which Amendment does not apply to pre-contact investigatory steps like that presented here (the decision to run a warrant check).
See Avery,
137 F.3d at 353 (“[A]n officer’s actions during the pre-contact stage cannot give rise to Fourth Amendment constitutional concerns because the citizen has not yet been ‘seized.’ ”). Even if the Fourth Amendment were implicated, any challenge to a search or seizure based on legitimate probable cause, but in which it is alleged the officer’s subjective motive was discriminatory, is doomed to fail.
See Whren,
517 U.S. at 813, 116 S.Ct. 1769 (unanimously rejecting such a challenge and holding that “[s]ubjeetive intentions play no role in ordinary, probable-cause Fourth Amendment analysis”). Though the Court left open the door to equal protection challenges in the same context, it gave no hint as to what the appropriate remedy would be.
See ibid.
Since we know from
Whren
that the evidence against Nichols would not be suppressed under the Fourth Amendment (even if the officers were improperly motivated by race), we are reluctant to graft that Amendment’s traditional remedy into the equal protection context. Indeed, we are aware of no court that has ever applied the exclusionary rule for a violation of the Fourteenth Amendment’s Equal Protection Clause
and we decline Nichols’s invitation to do so here. Rather, we believe the proper remedy for any alleged violation is a 42 U.S.C. § 1983 action against the offending officers.
See, e.g., Farm Labor Org. Comm. v. Ohio State Highway Patrol,
308 F.3d 523 (6th Cir.2002) (rejecting officer’s qualified immunity defense and affirming partial summary judgment in favor of Hispanic motorists who brought equal protection challenge under § 1983).
The Supreme Court has recently affirmed the adequacy of such suits to vindicate constitutional rights, and specifically rejected suppression as a remedy, in the context of a violation of the “knock-and-announce” rule under the Fourth Amendment.
See Hudson v. Michigan,
547 U.S. 586, 126 S.Ct. 2159, 165 L.Ed.2d 56 (2006). Speaking of the exclusionary rule in broad terms, the Court cautioned that “suppression of evidence ... has always been our last resort, not our first impulse” and emphasized that the rule’s “costly toll upon truth-seeking and law enforcement objec
tives presents a high obstacle for those urging its application.”
Id.
at 2163 (internal quotation omitted). The Court rejected the argument that a civil suit under § 1983 was an inadequate remedy for knock-and-announce violations, pointing out the “greatly expanded” number of public-interest law firms and lawyers specializing in civil rights grievances, and further noted that “increasing professionalism of police forces, including a new emphasis on internal police discipline” could provide a sufficient deterrent against abuses.
Id.
at 2167-68.
Hudson
reinforces our view that suppression is an extreme remedy, and that — prior to adopting such a remedy — a court must be convinced of the inadequacy of civil suits to safeguard against constitutional violations.
In contrast to
Hudson,
we note that here there was no intrusion at all on Nichols’s personal liberties by the initial actions of the officer. There was no search, no seizure, and only the use of the officer’s powers of observation from a place where he had a right to be, and his obtaining of information lawfully in the possession of the state. This contrasts strongly with the more intrusive and constitutionally invalid police actions in
Hudson,
where violation of the “knock-and-announce” rule still did not lead to the remedy of suppression of the evidence otherwise lawfully obtained. In sum, Nichols offers us no reason why, if civil suits are an adequate remedy for violation of the “knock-and-announce” rule, they cannot be for the decidedly less intrusive constitutional violation he alleges.
Moreover, even if suppression were an appropriate remedy in the abstract, it is clear that it would not be warranted on the facts of this case. In order to prevail on an equal protection claim, it is well established that a defendant “has the burden of proving the existence of purposeful discrimination.”
McCleskey v. Kemp,
481 U.S. 279, 292, 107 S.Ct. 1756, 95 L.Ed.2d 262 (1987) (internal quotation omitted). More specifically, he “must prove that the decisionmakers in
his
case acted with discriminatory purpose.”
Ibid.-, see also Avery,
137 F.3d at 355. Because it is often “difficult to prove directly the invidious use of race[,] ... inferences can be drawn from valid relevant statistical evidence of disparate impact or other circumstantial evidence.”
Avery,
137 F.3d at 355. Only after the defendant meets this initial burden of establishing a
prima facie
case must the government then “articulate a race-neutral reason for its action, or identify a compelling governmental interest in the race-based [action].”
Id.
at 356. We have previously cautioned and reiterate now that “[t]he defendant retains the ultimate burden of proving discrimination” and that “[o]nly in rare cases will a statistical pattern of discriminatory impact conclusively demonstrate a constitutional violation.”
Ibid,
(citing
McCles-key,
481 U.S. at 293-94 n. 12, 107 S.Ct. 1756).
Nichols cites no direct evidence of discrimination in his case and only the barest of circumstantial evidence. He asserts that “[t]he officer’s knowledge boils down to three criteria: early-morning hours, a congregation [of men], and black. Had this been a white congregation at 1:15 a.m. near another university [instead of the his-* torically black Tennessee State University], would an officer decide to run a check for warrants? No.” Appellant’s Br. at 20. Nichols then cites statistical data demonstrating that “roughly one third of young black men are under control of the criminal-justice system.”
Ibid.
But bald accusations and irrelevant generalized statistics do not even come close to constituting what is necessary to establish a
prima facie
case of an equal protection violation.
See McCleskey,
481 U.S. at 297, 107 S.Ct.
1756 (rejecting a statistical analysis far more detailed than that presented here as inadequate to establish a
prima facie
case). Nichols, however, states that “most significantly, in the face of this equal-protection claim, the Government failed to identify any nondiscriminatory reason for undertaking the warrant check. It offered no reason whatsoever.” Appellant’s Br. at 21. But absent the defendant establishing a
prima facie
case, the government is not required to offer any reason for its allegedly discriminatory action.
See McCles-key,
481 U.S. at 296 n. 18, 107 S.Ct. 1756 (noting the “Court’s longstanding precedents that hold that a prosecutor need not explain his decisions unless the criminal defendant presents a prima facie case of unconstitutional conduct with respect to his case”);
see also Avery,
137 F.3d at 356. Moreover, while it is true that Officer Des-lauriers never cited any specific reason in his testimony for requesting the warrant check on Nichols, it is reasonably clear from the entire context of the proceeding that, as the district court found, he did so based on the suspicious behavior of the individuals in attempting to avoid the police officers as they drove by, especially given the late hour and the number of individuals congregating around a vehicle with no apparent purpose.
Other than assertion, no argument at all is offered that a black officer would not have taken .the same actions, or that a late-night congregation of whites who took evasive action would not have elicited the same response.
Nichols argues that young black men attempting to avoid the police is “unremarkable” and cites two cases holding that such behavior fails to establish “reasonable suspicion.” Appellant’s Reply Br. at 15. But in deciding to simply run a check for outstanding warrants, an officer is not held to a “reasonable suspicion” standard.
See Avery,
137 F.3d at 358 (“An officer is not held to a suspicion of criminal activity standard when he embarks to investigate someone. The officer merely is prohibited from his pursuit if he acts based solely on race.”). Thus, the decision to check for outstanding warrants on Elbert Nichols did not require “reasonable suspicion” — indeed, it did not require any suspicion at all. All it required was that the decision not be based solely on Nichols’s race.
See ibid.
To hold otherwise would be to prohibit police from taking even the most basic initial investigatory steps absent some articulable suspicion, such as when officers simply have a “hunch” or are just following routine procedure — steps which, in this case, led to the apprehension of a dangerous fugitive.
Given Nichols’s failure to establish a
prima facie
case that Officer Deslauriers acted with discriminatory purpose, and our refusal to adopt his preferred remedy even if he had, his equal protection claim fails.
B
Nichols next argues that Officer Deslauriers’s search of the vehicle’s locked glovebox exceeded the permissible scope of a search incident to arrest under prevailing Supreme Court precedent. We disagree.
In
New York v. Belton,
453 U.S. 454, 101 S.Ct. 2860, 69 L.Ed.2d 768 (1981), the Su
preme Court drew a bright-line rule vis-a-vis the search of an automobile incident to the arrest of one of its occupants: the search extends to “the passenger compartment of that automobile,” including “any containers found within the passenger compartment....”
Id.
at 460, 101 S.Ct. 2860. The Court then more precisely defined the term “container”:
“Container” here denotes any object capable of holding another object. It thus includes
closed or open glove compartments,
consoles, or other receptacles located anywhere within the passenger compartment, as well as luggage, boxes, bags, clothing, and the like. Our holding encompasses only the interior of the passenger compartment of an automobile and does not encompass the trunk.
Id.
at 460 n. 4, 101 S.Ct. 2860 (emphasis added). Nichols argues that
Belton
left open the question of whether a
locked
glove box is also included within its definition of “container.” He urges this court to find that it is not, arguing that a locked glove box is more like the trunk of an automobile — the search of which
Belton
prohibits — than it is like a “closed or open” (but presumably unlocked) glove box — the search of which
Belton
permits. Appellant’s Br. at 25-26.
The Court justified the rule in
Belton
on the twin bases of officer safety and the need to preserve evidence.
Belton,
453 U.S. at 460-63, 101 S.Ct. 2860. Although it certainly seems impossible that Nichols could have, in a Houdini-like fashion, extricated himself from his handcuffs and escaped the patrol car to retrieve a weapon from a locked glove box, this court has made clear that, under prevailing Supreme Court precedent, the search-incident-to-arrest authority applies even where an item “is no longer accessible to the defendant at the time of the search[, s]o long as the defendant had the item within his immediate control near the time of his arrest....”
Northrop v. Trippett,
265 F.3d 372, 379 (6th Cir.2001). This interpretation has been affirmed in
Thornton v. United States,
541 U.S. 615, 124 S.Ct. 2127, 158 L.Ed.2d 905 (2004), which held that the rule in
Belton
applies even where a police officer does not make contact with a suspect until after he has already left his vehicle. The Court emphasized the bright-line nature of the rule, stating that “[t]he need for a clear rule, readily understood by police officers and not depending on differing estimates of what items were or were not within reach of an arrestee at any particular moment, justifies the sort of generalization which
Belton
enunciated.”
Id.
at 622,124 S.Ct. 2127.
In light of this precedent, it is no surprise that those circuit courts of appeal that have considered the specific question of a locked glove box are unanimous in holding that the
Belton
rule allows a search.
See United States v. Gonzalez,
71 F.3d 819 (11th Cir.1996);
United States v. Woody,
55 F.3d 1257 (7th Cir.1995);
United States v. McCrady,
774 F.2d 868 (8th Cir.1985). This court does not appear to have addressed the issue, but has approvingly cited a commentator’s proposed rule that “a passenger compartment for
Belton
purposes is properly viewed as including all space reachable without exiting the vehicle, excluding areas that would require dismantling the vehicle.”
United States v. Pino,
855 F.2d 357, 364 (6th Cir.1988) (citing 2 W. La Fave, SeaRch AND Seizure: A Treatise on the Fourth Amendment § 7.1, at 132 n. 9.2 (Supp.1982)) (internal quotation marks omitted). This rule would encompass a locked glove box.
Prevailing Supreme Court precedent logically dictates this conclusion. We therefore join the unanimous view of our sister circuits in holding that the search-incident-to-arrest authority permits an of
ficer to search a glove box, whether open or closed, locked or unlocked. Nichols’s Fourth Amendment claim therefore fails.
C
Lastly, Nichols argues that the inculpatory statements he made to Officer Deslauriers shortly after his arrest should be suppressed under
Miranda v. Arizona,
384 U.S. 436, 86 S.Ct. 1602, 16 L.Ed.2d 694 (1966). The government argues that Nichols impliedly waived his
Miranda
rights by voluntarily speaking with Officer Deslauriers after affirming that he understood these rights. It is the government’s burden to establish a waiver by a preponderance of the evidence.
Colorado v. Connelly,
479 U.S. 157, 168, 107 S.Ct. 515, 93 L.Ed.2d 473 (1986). We agree with the district court that the government met its burden in this case.
Since the government concedes that Officer Deslauriers never obtained an express waiver — either oral or written — from Nichols, this case is governed by the doctrine of implied waiver as set forth by
North Carolina v. Butler,
441 U.S. 369, 99 S.Ct. 1755, 60 L.Ed.2d 286 (1979), and its progeny. In
Butler,
the Supreme Court held that, absent an express waiver, a court must presume that a defendant has not waived his right to remain silent.
Id.
at 373, 99 S.Ct. 1755. Nevertheless,
[t]hat does not mean that the defendant’s silence, coupled with an understanding of his rights and a course of conduct indicating waiver, may never support a conclusion that a defendant has waived his rights. The courts must presume that a defendant did not waive his rights; the prosecution’s burden is great; but in at least some cases waiver can be clearly inferred from the actions and words of the person interrogated.
Ibid.
One such case where waiver may be clearly inferred is when a defendant, after being properly informed of his rights and indicating that he understands them, nevertheless does nothing to invoke those rights. For, while it does not require much to invoke the right to silence, it does require something that indicates a desire not to be questioned.
See Miranda,
384 U.S. at 445, 86 S.Ct. 1602 (“If the individual ... indicates in any manner that he does not wish to be interrogated, the police may not question him.”). Thus, a failure to invoke one’s right to remain silent— after being informed of and indicating an understanding of that right — functions as the equivalent of a waiver.
See United States v. Washington,
462 F.3d 1124, 1134 (9th Cir.2006) (“A person waives the right to remain silent if, after being informed of that right, the person does not invoke that right.”);
United States v. Cardwell,
433 F.3d 378, 389-90 (4th Cir.2005) (“[The defendant’s failure to invoke his rights ... left [the officer] free to interrogate him.... Because [the defendant] had been fully informed and indicated his understanding of his
Miranda
rights, his willingness to answer ... question^] is as clear an indicia of his implied waiver of his right to remain silent as we can imagine.”) The question, then, is whether Nichols here did anything to invoke his right to remain silent (i.e., to “indicate [] in any manner that he [did] not wish to be interrogated,”
Miranda,
384 U.S. at 445, 86 S.Ct. 1602). We conclude that he did not.
Nichols argues that his initial “refusal [to admit his identity] ... functioned as an invocation of his right to silence because he demonstrated a refusal to cooperate.” Appellant’s Br. at 32. Accordingly, he cites two cases that stand for the proposition that a refusal to give basic identifying information may serve as an invocation of one’s right to remain silent. Appellant’s Br. at 31 (citing
United States
v. Montana,
958 F.2d 516 (2d Cir.1992), and
Jacobs v. Singletary,
952 F.2d 1282 (11th Cir.1992)). These cases, however, are easily distinguished. In
Montana,
the suspect refused to utter
any words at all
in response to
any
questions initially put to him by the officers and only made incul-patory statements hours later.
Montana,
958 F.2d at 517-18. In
Jacobs,
the defendant refused to respond to the officer’s repeated questions about her name, telling him only that “it didn’t matter” and that “it didn’t make any difference.”
Jacobs,
952 F.2d at 1292. The officer continued to hound her for her name but “she repeatedly refus[ed] to speak at all” to the officer.
Ibid.
The defendants in both
Montana
and
Jacobs
simply refused to answer any questions put to them by the police. This is fundamentally different than affirmatively responding to an officer’s questions by lying, as Nichols did in this case. The district court understood this distinction, finding that Nichols’s “repeated denials of his identity were not refusals to answer all police questions. Rather, Defendant wished to, and did, communicate affirmatively with the police officers by making statements to them which he believed furthered his self-interest.”
There also is no evidence of any coercion on the part of the officers that would make Nichols’s action anything less than fully voluntary. After recognizing that Nichols would not be immediately forthcoming about his identity, Officer Deslauriers simply moved on to filling out the arrest paperwork and engaged Nichols in “general conversation” about it. At some point during this conversation regarding the paperwork, Nichols voluntarily confessed his identity but explained that the outstanding warrants were a “mistake.” He then made inculpatory statements about his ownership of the gun, stating that he kept it for self-protection. Nichols points to Officer Deslaurier’s statement that the defendant “got tired” as- evidence of coercion, Appellant’s Br. at 35, but this comment is at best ambiguous. The officer may simply have meant that Nichols eventually realized how ridiculous it was for him to continue to deny his identity despite his own mug shot staring him in the face. Moreover, the record illustrates that Nichols denied his identity for only a relatively short time before ultimately confessing (“several minutes”).
Finally, Nichols argues that Officer Des-lauriers’s checking a box on some paperwork indicating “no waiver” of
Miranda
means that the officer recognized that Nichols did not waive his rights, either expressly or impliedly. Appellant’s Br. at 35. It seems obvious, however, that this box on a standard police form is meant to apply to some kind of
express
waiver of
Miranda, e.g.,
a signed waiver form or perhaps at least an affirmative statement on the part of the suspect that he agrees to speak. It is difficult to imagine that the Metro Nashville Police Department designed this form so that, in the moments following an arrest, an officer would make an independent assessment of the defendant’s words and conduct, consider the principles elucidated by
Butler
and its progeny relating to implied waivers, then decide whether, under the totality of the circumstances, the defendant’s actions amounted to an implied waiver of his
Miranda
rights and check the box accordingly. Nichols’s argument on this point is thus unpersuasive.
Viewing the facts “in the light most likely to support the district court’s decision,”
Navarro-Camacho,
186 F.3d at 705, the district court correctly determined that Nichols — having been properly informed of and asserting that he understood his rights — did nothing to invoke those rights, and the government therefore met its bur
den of establishing that Nichols had impliedly waived his right to remain silent.
Ill
For the foregoing reasons, we AFFIRM the judgment of the district court.