Dante Winnick pled guilty to one count of being a felon in possession of a firearm in violation of 18 U.S.C. § 922(g)(1). The district court sentenced him to 53 months’ imprisonment, followed by three years of supervised release, and a $100 special assessment. Winnick appeals, arguing that his plea agreement is invalid because it was not made knowingly, voluntarily, and intelligently. Alternatively, he argues that the agreement is invalid because it conferred no benefit upon him. We affirm.
*719I.
On January 21, 2011, police officers found Winnick in possession of a loaded .380 caliber pistol. Winnick, who had previously been convicted of multiple felony offenses, was charged with being a felon in possession of a firearm. On April 17, 2011, Winnick signed a plea agreement and pled guilty to the charge. In the agreement, the government promised to recommend a three-level reduction for acceptance of responsibility under U.S.S.G. § 3E1.1. Winnick waived his right to appeal or challenge any within-Guidelines sentence. Both parties agreed not to seek a sentence outside the advisory range. The agreement also stipulated that Win-nick’s base-offense level was 24.
During the plea colloquy, the district court asked Winnick whether he was under the influence of any drugs or alcohol. Winnick answered that he had taken his “psych meds” the night before. The district court responded, “[m]ay I assume, sir, that those medications help you understand the proceedings?” Winnick answered, “Yes, ma’am.” The district court then asked defense counsel whether he thought Winnick understood what was happening during the plea colloquy. Defense counsel said yes. Winnick said later in the colloquy that he understood everything in the plea agreement. He also told the district court, however, that he had graduated high school and just gotten off probation — assertions that were later contradicted by the presentence investigation report (“PSR”). The report also indicated a history of mental and emotional health problems.
The district court accepted the PSR’s suggested base-offense level of 20 and sentenced Winnick to a 53-month term of imprisonment, followed by three years of supervised release, and a $100 assessment. The term fell within the Guidelines range of 46 to 57 months. After the district court denied his request to self-report at the sentencing hearing, Winnick questioned why he had not received a lower sentence due to his mental-health problems. The district court explained that it had considered these problems but that they did not warrant a departure.
II.
Winnick first argues that his plea is invalid because it was not entered into “knowingly, voluntarily, and intelligently.” United States v. Gardner, 417 F.3d 541, 544 (6th Cir.2005) (internal citation omitted). Rule 11 of the Federal Rules of Criminal Procedure “requires that a district court verify that the defendant’s plea is voluntary and that the defendant understands his or her applicable constitutional rights, the nature of the crime charged, the consequences of the guilty plea, and the factual basis for concluding that the defendant committed the crime charged.” United States v. Webb, 403 F.3d 373, 378-79 (6th Cir.2005). A defendant may challenge the district court’s failure to comply with Rule 11 even if the plea agreement in question allegedly waives the defendant’s right to appeal his sentence. See id. at 378 n. 1. But when a defendant waits until appeal to raise such a challenge — which is what Winnick has done here — we review only for plain error. See Gardner, 417 F.3d at 543.
A.
Winnick contends that the district court did not sufficiently inquire into the effects of the medication Winnick had taken the night before his plea colloquy. Once the district court learns that a defendant has recently ingested a substance capable of impairing his ability to knowingly and voluntarily plead, it must make an additional inquiry regarding the defendant’s competence. See United States v. Parra-Ibanez, *720936 F.2d 588, 596 (1st Cir.1991); United States v. Cole, 813 F.2d 43, 46 (3d Cir. 1987). Although the “better practice” is for the district court to ask what the drug is, how much of it has been taken, and its purpose and effects, the “critical question” is “whether the drugs — if they have the capacity to impair the defendant’s ability to plead — have in fact done so on this occasion.” United States v. Savinon-Acosta, 232 F.3d 265, 268 (1st Cir.2000).
In support of his argument that the district court’s inquiry into the effects of his “psych meds” was inadequate, Winnick relies on Cole and Parra-Ibanez. In Cole, upon learning that the defendant had ingested drugs the night before the plea colloquy, the district court failed to ask anything more about the drugs. 813 F.2d at 45. In fact, the record was unclear whether the district court noticed the defendant’s admission of drug use at all. Id. at 46. In Parra-Ibanez, after learning that the defendant had taken medication less than 24 hours before the plea colloquy, the court merely asked what medication the defendant was taking and whether the medication helped the defendant control his nerves. 936 F.2d at 591. Though the district court later inquired into the defendant’s general ability to understand the proceedings, it never asked about the specific impact of the medication on defendant’s competence. Id. at 592. In concluding that such an inquiry was insufficient, the First Circuit explained that the district court’s previous knowledge of the defendant’s history of drug use, depression, and attempted suicide, obtained through a competency hearing only a week before the plea colloquy, “enhanced” the obligation of further inquiry. Id. at 596 n. 16.
The district court made a more thorough inquiry here. Specifically, the court did ask the “critical question” whether “those medications help you understand the proceedings.” In United States v. Morrisette, the First Circuit held that asking the defendant whether recently-ingested medication affected his ability to understand the proceeding — nearly the identical question asked by the district court here — was sufficient to establish the voluntary and knowing nature of the defendant’s guilty plea. 429 F.3d 318, 322 (1st Cir.2005). Moreover, unlike in Parra-Ibanez, there is no indication here that the district court had any knowledge of the defendant’s history of mental illness at the time of the plea colloquy. Thus, the “enhanced” obligation of further inquiry required in Parra-Ibanez was not required here. See id.
A defendant’s behavior during a plea colloquy may also confirm or undermine his assurances of competency. See Savi-non-Acosta, 232 F.3d at 269 (internal citation omitted). Winnick argues that his false statements regarding whether he graduated high school and whether he was still on probation should have alerted the district court that he was incompetent to plead guilty. But nothing in the record indicates that these answers were the result of incompetency, as opposed to misstating the truth. Moreover, Winnick’s behavior throughout the plea colloquy, such as when he cited the district court’s ability to depart from the Guidelines range, reveals his ability to comprehend the proceedings. Thus, the district court’s inquiry, reinforced by Winnick’s behavior throughout the colloquy, demonstrates that the district court did not err in its conclusion that Winnick entered his guilty plea knowingly and voluntarily.
B.
Winnick also argues that his plea was not made knowingly and voluntarily because he did not understand the consequences of his plea agreement. He first *721contends that, because the base-offense level stipulated in the plea agreement was different from the base-offense level determined by the PSR and accepted by the district court, he could not have understood the consequences of the agreement. But when a plea agreement contemplates a higher offense level than actually applied, as was the case here, the plea is valid so long as the defendant has been informed of the statutory maximum sentence. See United States v. Parrella, 448 Fed.Appx. 591, 592 (6th Cir.2012) (unpublished). Winnick was informed of the ten-year statutory maximum here, and thus the later downward adjustment of the base-offense level is irrelevant.
Winnick further contends that he misunderstood the consequences of his plea because he erroneously believed that he would receive a downward departure for his mental health. During the sentencing hearing, however, Winnick conceded that he had reviewed the PSR with his attorney and that he had no objections to the report, whose calculation did not include any downward departure. Thus, Winnick failed to establish that he misunderstood the consequences of his plea agreement.
C.
Finally, Winnick argues that his plea agreement is invalid because it conferred no benefit upon him. The existence of a valid plea agreement is a question of fact, and we review for clear error. See United States v. Quesada, 607 F.3d 1128, 1131 (6th Cir.2010). A plea agreement must confer some benefit upon the defendant. See United States v. Randolph, 230 F.3d 243, 249 (6th Cir.2000). The agreement is valid even if this benefit is minimal. See, e.g., United States v. Brunetti, 376 F.3d 93, 96 (2d Cir.2004) (enforcing a plea agreement made in exchange for a mere chance at a reduced sentence); United States v. Wesley, 13 Fed.Appx. 257, 260 (6th Cir.2001) (per curiam) (holding that the government’s promise to recommend a sentence at the lower end of and a fine within the Guidelines range and to not oppose a three-level reduction for acceptance of responsibility was sufficient consideration for a plea agreement).
Winnick benefited from the plea agreement here. In exchange for the agreement, the government promised to recommend a three-level reduction for acceptance of responsibility. This full three-level reduction may only be awarded upon government motion. See United States v. Smith, 429 F.3d 620, 627 (6th Cir.2005). The guarantee of such a motion conferred a benefit on Winnick. The same is true of the government’s agreement not to request a sentence above the Guidelines range.
The district court’s judgment is affirmed.