An officer on routine patrol in Ft. Wayne, Indiana, at 2:30 A.M. saw a car driving unusually slowly on a residential street. Out of curiosity he checked its license plate using a computer terminal in the patrol car and learned that it matched a different auto. That violation of the vehicular code justified a stop, independent of any suspicion that a valid plate had been attached to a stolen car to avoid detection. The driver claimed not to be carrying a license or any other identification; he gave his name as Hector Bazan. After smelling alcohol on the driver’s breath, the officer administered a breathalyzer test; the results implied that the driver was intoxicated. A quick check on the patrol car’s terminal showed that no “Hector Bazan” was licensed to drive in Indiana. At this point the officer had probable cause to believe that “Bazan” had committed at least one traffic infraction (driving a car that that lacked proper license plates) and two crimes (driving without a license and driving under the influence of alcohol).
Fort Wayne’s police department discourages “John Doe” bookings, so the officer was anxious to pin down the driver’s name. He told the driver that if he could prove his identity, then he would receive citations and summonses; otherwise he would be fingerprinted and booked at the station-house. “Bazan” said that he had identification at home and offered to show the officer where he lived. The officer handcuffed “Bazan” and put him in the back of the squad car for the drive. Once at home, “Bazan,” still in handcuffs, unlocked the front door and entered; the officer followed. (By then a second officer had joined the first; we ignore this detail.) The district court found that the driver “did not tell the officers to stay outside, nor did he invite them in.” “Bazan” walked through several rooms, trying in vain to find the identification he was seeking. Tagging along, the officer saw evidence that the house was a bogus-ID mill. Instead of allowing “Bazan” to keep searching, the officer told him to sit down while the police obtained a search warrant — which they did, by telephone. Executing the warrant, the police seized evi*650dence that the occupants of the house were making fraudulent documents. They also discovered who the driver really is. Apparently he lacked enough confidence in his handiwork to carry one of the-fakes himself, but he had strong reason not to tote anything bearing his real name. An open shoebox contained court papers with the name Ricardo Garcia in the caption. Using the squad car’s terminal a third time, the police found that Garcia was evading two warrants for his arrest. The crime: forgery.
A federal indictment charged Garcia with possessing document-making implements with the intent to produce false identification. See 18 U.S.C. § 1028(a)(5). The district court granted his motion to suppress the evidence seized from his home, ruling that the warrant depends on information that the fourth amendment barred the police from learning. As the district judge understood the situation, Garcia had not been arrested but instead had been detained on reasonable suspicion. See Terry v. Ohio, 392 U.S. 1, 88 S.Ct. 1868, 20 L.Ed.2d 889 (1968). Although the judge recognized that police may follow an arrested suspect wherever he goes, even inside a residence, see Washington v. Chrisman, 455 U.S. 1, 6-7, 102 S.Ct. 812, 70 L.Ed.2d 778 (1982), she held that they are forbidden to do the same with' persons stopped under Terry. The United States has taken an interlocutory appeal, which the Criminal Appeals Act authorizes. See 18 U.S.C. § 3731 ¶ 2.
The district court’s premise is false, and the bad premise spoiled the conclusion. Garcia had been arrested. His traffic stop was itself an arrest on probable cause. See Whren v. United States, 517 U.S. 806, 116 S.Ct. 1769, 135 L.Ed.2d 89 (1996). That is why, we have held, it is inappropriate to treat investigations following traffic stops as governed by Terry, when the stop rests on probable cause to believe that an offense has been committed. See United States v. Childs, 277 F.3d 947, 952-54 (7th Cir.2002) (en banc). This stop was supported by probable cause, and soon probable cause to believe that Garcia had committed two more offenses turned up. Custody had ample support.
To call particular custody an “arrest” does not necessarily mean that a given search or seizure is reasonable. No matter how much custody may be permissible - Atwater v. Lago Vista, 532 U.S. 318, 121 S.Ct. 1536, 149 L.Ed.2d 549 (2001), holds that police may make full custodial arrests for fine-only offenses, so there is . no doubt that the officer could have taken Garcia to the stationhouse without ado— the reasonableness of a search or seizure depends on what actually happens rather than what could have happened. See Childs, 277 F.3d at 953. That is why police may not conduct full searches of drivers, passengers, and vehicles in all routine traffic stops. See Knowles v. Iowa, 525 U.S. 113, 119 S.Ct. 484, 142 L.Ed.2d 492 (1998). Most drivers are given citations and sent on their way. Because the principal justifications for full searches are the need to detect risks to the arresting officers and to preserve evidence that suspects could destroy on the way to the lockup, there is slight warrant for intrusive steps when detention is brief and the drivers (and most evidence) will soon depart. Compare Knowles with Gustafson v. Florida, 414 U.S. 260, 94 S.Ct. 488, 38 L.Ed.2d 456 (1973), and United States v. Robinson, 414 U.S. 218, 94 S.Ct. 494, 38 L.Ed.2d 427 (1973).
Garcia was not among those covered by a catch-and-release regimen, however. He could not produce a driver’s license, and Gustafson holds that a driver who lacks a license is subject to full custodial arrest and thorough search. Moreover,- Garcia *651was inebriated; the police could not let him drive away and endanger others on the road. So they took him into custody. Both in the squad car and during the tour of his home Garcia was in handcuffs. It would have been folly for the police to let him enter the home and root about unobserved. What if Garcia set out to look for weapons rather than identification? So it was reasonable to go with him if he entered at all — no less reasonable than in Chrisman itself. A police officer stopped Overdahl, a university student, carrying a bottle of gin. As Overdahl was under 21 and not entitled to possess or drink liquor, he had committed an offense. The officer asked for identification; Overdahl volunteered to retrieve it from his dormitory room. Standing in the door and observing while Overdahl searched for ID, the officer saw Chrisman, Overdahl’s roommate, committing a drug offense. The Court held that the officer had acted reasonably, so Chrisman could be prosecuted based on what the officer had seen. If it was reasonable for the officer to keep Overdahl in view, it was no less reasonable to keep Garcia in view — for Garcia’s offenses were more serious, and the risk that he would retrieve a weapon or take an opportunity to flee was appreciably greater. (Note, too, that the Court treated Overdahl as under arrest, not as the target of a Terry stop. The police had probable cause to think that Overdahl had committed a crime; just so with Garcia.)
That leaves only the question whether it was unreasonable to give Garcia the choice of looking for identification. Yet increasing a suspect’s options cannot harm him; additional options provide benefits, and as long as suspects are free to refuse they cannot be made better off by a rule forbidding the offer. Many persons situated similarly to Garcia (but not having evidence of crime in plain view at home) welcome the opportunity to find their drivers’ licenses and thus avoid full custodial arrests. Perhaps drink prevented Garcia from appreciating that the police would keep their eyes open, and that his situation would go from bad to worse, but when making the offer and tagging along the police did not know this; a suspect’s poor choice does not render unconstitutional an officer’s objectively reasonable offer.
The district judge was led astray by the language the police used at the hearing. Officer Bonar, who stopped Garcia’s car, testified that he did not plan to arrest the driver unless he was unable to provide positive identification, and that even while in handcuffs Garcia was “detained” rather than “under arrest.” From this the district judge concluded that it must have been a Terry stop; there is no other alternative to “arrest.” Fourth amendment jurisprudence, however, is objective. See Whren, supra, 517 U.S. at 811-16, 116 S.Ct. 1769. See also, e.g., Maryland v. Pringle, 540 U.S. 366,-, 124 S.Ct. 795, 800, 157 L.Ed.2d 769 (2003); Ohio v. Robinette, 519 U.S. 33, 38-39,117 S.Ct. 417, 136 L.Ed.2d 347 (1996); Maryland v. Macon, 472 U.S. 463, 470-71, 105 S.Ct. 2778, 86 L.Ed.2d 370 (1985); Scott v. United States, 436 U.S. 128, 136, 98 S.Ct. 1717, 56 L.Ed.2d 168 (1978). It does not matter what Bonar was thinking or planning. Reasonableness depends on facts, not labels. Officer Bonar evidently uses the word “arrest” to mean what the Supreme Court calls a “full custodial arrest” — a trip to the stationhouse for booking and incarceration. He uses the word “detention” to mean what the Supreme Court calls an arrest. Police officers’ diction does not affect the constitutional inquiry. Definitions do not matter either. The fourth amendment asks whether a particular search was “reasonable” rather than whether a suspect was “under arrest.” If a person in custody on probable cause *652elects to hunt for identification at home in order to reduce the custody’s duration, it is reasonable for police to keep him in view to ensure that credentials are the only object of the expedition. Thus the police were entitled to be in a place where evidence of crime was in plain view; their observations were lawful; and as they did not seize that evidence until a warrant had issued, the exclusionary rule has no role to play.
Reversed