ORDER

After serving a 46-month prison sentence for unlawful possession of a firearm by a felon, see 18 U.S.C. § 922(g)(1), Warren G. Griffin was released in January *5542000 and began a three-year term of supervised release. In June 2000, the United States Probation Office filed a petition to revoke Mr. Griffin’s supervised release, alleging that he had violated the terms of his release by possessing a firearm, associating with a convicted felon, and failing to gain lawful employment. Specifically, the petition alleged that on June 12, 2000, an East St. Louis, Illinois detective observed Mr. Griffin in possession of a .357 Magnum revolver during a traffic stop, and that on that day Mr. Griffin was with Darryl V. Russell, a felon. The petition also alleged that Mr. Griffin was unemployed the entire time he was on supervised release. After an evidentiary hearing, the district court found that Mr. Griffin violated the conditions of his release and returned him to prison for 24 months. Mr. Griffin appeals, contending that the government failed to prove by a preponderance of the evidence that he violated the terms of his release. We affirm.

I.

At the revocation hearing, Detective Desmond Williams testified for the government that around 11:00 p.m. on June 12, 2000, he observed a blue four-door Pontiac Grand Am speeding down a street in East St. Louis. Detective Williams pulled the car over, directed his spotlight into the vehicle and saw two men inside. The detective first approached the driver’s side and identified the driver as Darryl Russell. As he was speaking with Mr. Russell, Detective Williams noticed the handle of a revolver protruding from the waistband of the passenger’s trousers. The detective drew his weapon and instructed the men to keep their hands where he could see them. He then opened the rear passenger door, reached inside the car between the front seats and tried to remove the gun from the passenger’s waistband. When Detective Williams placed his hand on the gun, the passenger grabbed the detective’s hand. The detective then pointed his weapon at the passenger and told him to release his hand or he would shoot him. The passenger let go of the detective’s hand, jumped out of the car, and fled. Detective Williams then handcuffed Mr. Russell and called for assistance.

The detective identified the gun he recovered from the passenger as a loaded Ruger .357 Magnum revolver. Detective Williams then conducted an inventory search of the car, which yielded a traffic citation and a bond sheet in the name of Warren Griffin on the front passenger seat. The detective also discovered an envelope bearing the name Warren Griffin and containing recently developed photographs. According to Detective Williams, one of the photographs depicted the passenger who had just fled the vehicle.

Detective Williams later obtained a booking photograph of Warren Griffin and identified him as the passenger. The detective also identified Mr. Griffin in court as the passenger he had seen on June 12, stating that he had “no doubt” it was the same person. (Tr. 9.) Additionally, Detective Williams testified that after he ran the plates on the car and learned that it was a rental vehicle, he obtained the rental agreement and discovered that Warren Griffin had rented the car.

Mr. Griffin’s probation officer, Christopher Origliosso, testified that he informed Mr. Griffin that he could not possess a firearm, and Mr. Griffin signed two documents stating that he had been so advised. Mr. Origliosso also ascertained that the driver of the car, Mr. Russell, had been convicted of armed robbery and aggravated battery with a weapon and had served a state prison sentence. Additionally, the probation officer testified that Mr. Griffin had not obtained employment since he had *555been on supervised release, although he had been repeatedly reminded of this condition. Mr. Origliosso acknowledged, however, that Mr. Griffin may have been under the impression that he had six months to get a job (or until July 2000), before he would be considered in violation of the terms of his supervised release.

Mr. Griffin presented several witnesses in an effort to show that it was not him but a person known as “Boo” who was the passenger in his rental car on June 12. First, Gregory Parker testified that Mr. Griffin had been helping out in his variety store that day and left sometime between 9:45 and 10:10 p.m. Mr. Parker recalled that Mr. Griffin was waiting for a ride that evening, but he did not see who gave him a ride or what car picked him up. Mr. Parker also stated that his store was a mile or two from the location of the traffic stop.

Charles Gray testified that Mr. Griffin called him at 10:30 p.m. on what he believed was June 12 to ask for a ride home from the variety store because another ride had not showed up. Mr. Gray, who lived about three to five minutes from the store, picked Mr. Griffin up and drove him to his home in Belleville, estimating that he dropped Mr. Griffin off sometime between 10:30 and 11:00 p.m. On the way home, Mr. Griffin mentioned to him that he was worried about where his Grand Am was.

Mr. Griffin then called Isaac Windom, whose nickname was Boo. Mr. Windom exercised his Fifth Amendment right against self incrimination. Brenda Tripp, a defense investigator, testified that Mr. Griffin’s wife told her where to contact Boo. According to Ms. Tripp, Boo told her that he was the passenger in Mr. Griffin’s car on the night of June 12. Boo stated that he did not know the driver of the car, but he had been with a group of people when he learned that the driver was going to the store. Boo described to Ms. Tripp how he got into the car to accompany the driver to the store, and shortly thereafter the police stopped them. The officer saw that he had a gun and when he tried to retrieve it, Boo ran from the car.

Mr. Griffin’s wife, Joclyn Griffin, testified that Mr. Gray gave her husband a ride home on June 12 and that he arrived at about 11:00 p.m. She stated that Mr. Griffin was upset and that he made a telephone call asking someone to have his car brought back. The next day, her husband told her that the car was in the tow yard.

Mr. Griffin’s attorney proffered the statement of Darrell Russell, who exercised his Fifth Amendment right against self-incrimination. According to the attorney, Mr. Russell told her that on June 12 he borrowed a car from “James” to go to the store, and someone named Boo accompanied him. En route to the store, the traffic stop occurred. Mr. Russell stated it was Boo, not Mr. Griffin, who was the passenger carrying the gun that evening. In response to the district court’s inquiry, Mr. Griffin’s attorney stated that Mr. Griffin had loaned the rental car to his friend “James” on June 12, although she could not locate “James” for the hearing.

In rebuttal, the government called Deputy United States Marshal Sean Newlin, who testified that during an interview after the traffic stop Mr. Russell told him that he was walking down the street at about 9:00 p.m. that evening when “James” picked him up. Additionally, Deputy Marshal Newlin testified that when he interviewed Mr. Griffin after his arrest, Mr. Griffin never stated that he had called Charles Gray for a ride that evening; rather, Mr. Griffin told him that he just happened to be at the variety store when Mr. Gray stopped by. Further, Mr. Grif*556fin stated that “he was not stopped by any skinny policemen.” (Tr. 68.)

The district court first discounted the testimony of Charles Gray, finding it suspect that he could remember the precise date and time he picked up Mr. Griffin from the store but was unsure about other dates and times. Further, Mr. Gray’s testimony contradicted Mr. Griffin’s statement to Deputy Marshal Newlin that Mr. Gray happened to come by the store that night. The court also disbelieved the testimony of both Jocelyn Griffin and Charles Parker due to their relationship with Mr. Griffin, and their convenient ability to recall exact times on the night in question. Additionally, the court was concerned that, although the Griffins were able to identify and produce some of the participants in the chain of events Mr. Griffin described, they had been unable to locate their friend “James.”

In contrast, the district court found the testimony of Detective Williams to be “completely credible.” (Tr. 78.) The court noted that the detective had sufficient opportunity to observe the passenger of the car that evening and that the spotlight enabled him to clearly see the passenger. Further, the court observed that Detective Williams identified the passenger from the photograph found inside the envelope bearing the name Warren Griffin, from Mr. Griffin’s booking photograph, and again in court.

The district court thereby found by a preponderance of the evidence that Mr. Griffin violated the terms of his supervised release by possessing a firearm and associating with a felon. The court did not find, however, that Mr. Griffin violated the condition that he work regularly at a lawful occupation because Mr. Griffin may have been under the impression that he had six months to find a job. The court then revoked Mr. Griffin’s supervised release and sentenced him to 24 months’ imprisonment.

II.

On appeal, Mr. Griffin contends that the district court’s findings at the revocation proceeding were not supported by a preponderance of the evidence. The government bears the burden of showing that the defendant violated the terms of the supervised release. United States v. Goad, 44 F.3d 580, 585 (7th Cir. 1995). The district court may revoke supervised release upon finding “by a preponderance of the evidence that a person violated a condition of supervised release,” see 18 U.S.C. § 3583(e)(3); Goad, 44 F.3d at 585, and we review a district court’s decision to revoke a term of supervised release for an abuse of discretion, United States v. Young, 41 F.3d 1184, 1186 (7th Cir. 1994); United States v. Dillard, 910 F.2d 461, 464 (7th Cir. 1990).

Mr. Griffin argues in particular that the district court “over-credited” Detective Williams’s testimony because his identification of the passenger in the vehicle was based on a short-lived encounter, and because the presence of a weapon during the encounter drew the detective’s focus away from the passenger. Thus, Mr. Griffin contends, the district court should have concluded that Detective Williams’s identification of the passenger was inaccurate.

Mr. Griffin’s argument cannot prevail, however, because we review the district court’s findings of fact and credibility determinations only for clear error. United States v. Woods, 233 F.3d 482, 484 (7th Cir. 2000). We are hesitant to second-guess the sentencing judge on issues of credibility because he or she has had the best opportunity to observe the witnesses, both their verbal and non-verbal behavior. *557Id.; United States v. Stokes, 211 F.3d 1039, 1045 (7th Cir. 2000). “When the sentence rests on testimony under oath, ... it is enough that the judge believe the witness — unless the testimony is illogical or contradicted by documents or other physical evidence, making it clearly erroneous to accept the witness’s version of events.” United States v. Torres-Ramirez, 213 F.3d 978, 980-81 (7th Cir. 2000). Here, the district court found Detective Williams’s testimony “completely credible” and “not shaken by [Mr. Griffin] on cross examination.” (Tr. 78.) The court noted that the detective had an opportunity to observe the passenger, and that the spotlight provided sufficient illumination. Further, the court observed that Detective Williams identified Mr. Griffin as the passenger on three separate occasions — from the photograph found in the car, from Mr. Griffin’s booking photograph, and again in court.

Mr. Griffin nonetheless argues that the evidence he presented far outweighed Detective Williams’s testimony. But we have observed that “[w]hen confronted with conflicting testimony, sentencing judges ‘are fully capable of considering the motivations of the witnesses in weighing conflicting evidence and, because they have had an opportunity to assess the demeanor of the witnesses, are in a better position than this court to make credibility determinations.’ ” United States v. Kroledge, 201 F.3d 900, 910 (7th Cir. 2000) (citation omitted). Here, the district court discounted the evidence presented by Mr. Griffin based in part on his relationships with the witnesses. Additionally, “at sentencing the testimony of one witness ... is sufficient to support a finding of fact.” United States v. Lindsey, 30 F.3d 68, 70-71 (7th Cir. 1994). Thus, Detective Williams’s testimony, standing alone, was enough for the district court to find by a preponderance of the evidence that Mr. Griffin violated the terms of his supervised release. Accordingly, we AFFIRM the judgment of the district court.