Defendant Alexis Miranda-Sotolongo challenges both his conviction and his sentence for being a felon in possession of a firearm, in violation of 18 U.S.C. § 922(g)(1). First, he argues that the district court erred in denying his motion to suppress the guns used to convict him, contending that the police lacked reasonable suspicion to conduct the traffic stop that led to the discovery of the guns. We affirm the denial of the motion to suppress. The officer based the stop on the fact that the number on the defendant’s car’s temporary registration tag did not appear in the relevant law enforcement database. That discrepancy gave the officer a reasonable suspicion that the car was either stolen or otherwise not properly registered.
*666Second, the defendant argues that several special conditions of supervised release are too vague and not justified. Although he did not raise these challenges in the district court and the conditions had often been imposed without controversy, recent decisions from this court require us to remand this case for reconsideration of those conditions of supervised release.
I. Fourth Amendment Challenge to the Traffic Stop
Miranda-Sotolongo’s encounter with the police began on Labor Day, Monday, September 2, 2013, when Officer Jared Johnson spotted him driving a white Cadillac on an interstate highway in Bloomington, Illinois. Miranda-Sotolongo had not been speeding, swerving, or committing any moving violation. What caught Officer Johnson’s attention was an Indiana temporary vehicle registration tag that looked odd. He testified that this tag was unlike any Indiana registration tag he had seen before and that in his experience temporary Indiana tags were normally “in the back of a window, not a piece of paper where the license plate normally goes.”
Officer Johnson decided to check the registration number in the relevant database. When first his own check and then a dispatcher’s separate check of the database found no record of the registration, Johnson made a traffic stop to investigate whether the tag might be a forgery designed to hide a stolen or otherwise unregistered vehicle. When Officer Johnson asked Miranda-Sotolongo for his license, he admitted that he was driving on a suspended license. The officer arrested him. During a later inventory search, the police discovered the two guns that led to defendant’s conviction.
Miranda-Sotolongo argues on appeal that the initial stop violated the Fourth Amendment and that the district court erred by denying his motion to suppress the guns as evidence. We review the district court’s factual findings for clear error and review de novo whether the stop was reasonable under the Fourth Amendment. See United States v. Uribe, 709 F.3d 646, 649 (7th Cir. 2013). A traffic stop is reasonable when the officer has reasonable suspicion that criminal activity is afoot, see id. at 649-50, citing Terry v. Ohio, 392 U.S. 1, 21-22, 88 S.Ct. 1868, 20 L.Ed.2d 889 (1968), which can extend to violations' of traffic laws, as Uribe makes clear. See also Rodriguez v. United States, 575 U.S. -, 135 S.Ct. 1609, 1614, 191 L.Ed.2d 492 (2015) (routine traffic stop is more analogous to Terry stop than to formal arrest); Heien v. North Carolina, 574 U.S. -, 135 S.Ct. 530, 536, 190 L.Ed.2d 475 (2014) (reasonable suspicion that driver is breaking traffic law can justify traffic stop).
Reasonable suspicion requires more than a hunch. The officer must be able to identify some “particularized and objective basis” for thinking that the person to be stopped is or may be about to engage in unlawful activity. United States v. Cortez, 449 U.S. 411, 417, 101 S.Ct. 690, 66 L.Ed.2d 621 (1981). The Fourth Amendment requires an officer making a stop to point to “specific and articulable facts” that suggest unlawful conduct. See Uribe, 709 F.3d at 650, quoting Terry, 392 U.S. at 21, 88 S.Ct. 1868.
The factual basis for the stop identified by the officer here — and the one relied upon by the government and the district court — is that Miranda-Sotolongo’s vehicle registration did not appear in the law enforcement database. The district court reasoned that because the officer was unable to verify that the car was registered, he had a reasonable suspicion that the temporary tag was a forgery designed to mask an unregistered or stolen car.
*667Before we address that basis for the officer’s suspicion, we first consider Miranda-Sotolongo’s argument that the government was not entitled to rely at all on the database information to justify the stop. He argues that the actual reason he was pulled over was only the officer’s mistaken belief that placing a temporary paper registration tag in the normal license-plate holder violated Indiana law. At the suppression hearing, the officer testified that, in .his experience, temporary Indiana registration tags were normally “in the back of a window, not a piece of paper where the license plate normally goes.” This suspicion that there was something strange about this particular tag led the officer to check the database to verify it.
Although one can often see Indiana temporary registration tags in rear windows, it is clear that Indiana law actually required Miranda-Sotolongo to place the temporary paper registration tag exactly where he did — where a normal license plate goes and not in the rear window. See Meredith v. State, 906 N.E.2d 867, 872-73 (Ind. 2009). Miranda-Sotolongo is correct in theory, then, that if the only basis for the stop had been the officer’s suspicion that the display of the registration tag somehow violated Indiana law, we could uphold the stop only if the officer’s mistaken understanding of the law about how to display a temporary tag was a reasonable one. See Heien v. North Carolina, 574 U.S.-, 135 S.Ct. 530, 539, 190 L.Ed.2d 475 (2014) (“The Fourth Amendment tolerates only reasonable mistakes, and those mistakes — whether of fact or of law — must be objectively reasonable.”).
We need not decide whether the Illinois officer’s mistaken view of Indiana traffic law was reasonable. Although the location of the tag was what first caught Officer Johnson’s eye, the record makes clear that he did not stop Miranda-Soto-longo’s vehicle until after two computer checks failed to verify that the vehicle was temporarily registered as the tag indicated. The reason for the stop was not to investigate the placement or form of the tag but to verify that the tag was not disguising a stolen or unregistered vehicle. The fact that Indiana has chosen to use pieces of paper that appear easy to forge as temporary tags might have contributed to the officer’s suspicions. But Officer Johnson also had information that this particular temporary tag did not appear in the database it should have been in. Finding reasonable suspicion here would not allow the police to stop just any vehicle with a temporary Indiana registration tag.
To avoid this logic, Miranda-Sotolongo also argues that the police were not entitled to consider the information from the law enforcement database in the first place. He argues that the information was discovered by a search that was itself unreasonable under the Fourth Amendment. In his view, because the only reason for the computer check was either a random “spot check” or the officer’s mistaken belief that the temporary tag did not comply with Indiana law, there was no individualized suspicion of wrongdoing or other justification for the officer’s decision to check his registration.
A police officer’s check of a vehicle registration in a database is not a Fourth Amendment search, as every other circuit that has considered this issue has held. See, e.g., United States v. Diaz-Castaneda, 494 F.3d 1146, 1150-52 (9th Cir. 2007); United States v. Ellison, 462 F.3d 557, 561-63 (6th Cir. 2006); Olabisiomotosho v. City of Houston, 185 F.3d 521, 529 (5th Cir. 1999); cf. United States v. Walraven, 892 F.2d 972, 974 (10th Cir. 1989) (“Because they are in plain view, no privacy interest exists in license plates.”), citing United States v. Matthews, 615 F.2d 1279, *6681285 (10th Cir. 1980). The registration check involves only checking publicly displayed registration information against official public records. We see no difference between such checks and comparing, for example, a photograph of a person against mug shots or latent fingerprints against FBI fingerprint records.
In this case, observing and recording the registration number was not a search within the meaning of the Fourth Amendment. Nor was it a search to use the registration tag number (in which defendant had no reasonable expectation of privacy) to retrieve the registration information present in the law enforcement database. See Diaz-Castaneda, 494 F.3d at 1152; Ellison, 462 F.3d at 562-63; but see Ellison, 462 F.3d at 566-71 (Moore, J., dissenting) (arguing that police use of databases to investigate vehicles and drivers threatens privacy interests to extent that should be subject to Fourth Amendment scrutiny). Because the police conducted a check of a database containing only non-private information and did so using only registration information that could be seen by any member of the public, the police did not conduct a Fourth Amendment search. Regardless of whether the police had an articulable suspicion that Miranda-Sotolongo was engaged in unlawful conduct, they would be able to rely on the information obtained from that search as a basis for the stop.1
Miranda-Sotolongo argues further that even if the police did not violate his rights by finding the absence of registration information in the database, that absence could not support a reasonable suspicion that he was violating Illinois law. Illinois requires vehicles driven on its roads to be registered, whether in Illinois itself or in the home state of an out-of-state driver. 625 ILCS 5/3-401(a); 625 ILCS 5/3-402(B)(2)(a). For that reason, we and other courts have previously upheld stops based on the absence of car registration information in the computer database. See, e.g., United States v. Mounts, 35 F.3d 1208, 1213 & n. 4 (7th Cir. 1994); United States v. Cortez-Galaviz, 495 F.3d 1203, 1205-06 (10th Cir. 2007); United States v. Stephens, 350 F.3d 778, 780 (8th Cir. 2003); cf. Delaware v. Prouse, 440 U.S. 648, 663, 99 S.Ct. 1391, 59 L.Ed.2d 660 (1979) (noting that traffic stop is justified when there is reasonable suspicion “that an automobile is not registered”).
Miranda-Sotolongo points out some innocent explanations for the vehicle’s registration not appearing in the law enforcement database. For example, there could be a delay between a person’s registration of a newly purchased ear and the updating of the state records. Such a delay might have explained the discrepancy here. Miranda-Sotolongo was stopped on the Monday of a holiday weekend. In fact, Officer Johnson, in explaining why he made the stop, recognized the possibility that the car was recently purchased (as Miranda-Soto-longo told him it had been) and made clear that he stopped the car to resolve the ambiguity about whether it was newly purchased or stolen or unregistered.
Police officers encounter situations of uncertain legality all the time. Uncertainty does not always justify a Terry stop or a traffic stop, which can intrude *669substantially on a person’s privacy and dignity. We have explained that a “suspicion so broad that [it] would permit the police to stop a substantial portion of the lawfully driving public” is not reasonable. United States v. Flores, 798 F.3d 645, 649 (7th Cir. 2015) (possibility that license plate frame covered unknown information on license plate did not justify traffic stop); accord, United States v. Paniagua-Garcia, 813 F.3d 1013, 1014-15 (7th Cir. 2016) (citing Flores, possibility that driver was using cell phone for unlawful texting rather than lawful phone call or other lawful purpose did not justify traffic stop).
Reasonable suspicion, however, does not require the officer to rule out all innocent explanations of what he sees. The need to resolve ambiguous factual situations — ambiguous because the observed conduct could be either lawful or unlawful — is a core reason the Constitution permits investigative stops like the one at issue here. See Illinois v. Wardlow, 528 U.S. 119, 125, 120 S.Ct. 673, 145 L.Ed.2d 570 (2000) (“Even in Terry, the conduct justifying the stop was ambiguous and susceptible of an innocent explanation. The officer observed two individuals pacing back and forth in front of a store, peering into the window and periodically conferring. All of this conduct was by itself lawful, but it also suggested that the individuals were casing the store for a planned robbery. Terry recognized that the officers could detain the individuals to resolve the ambiguity.”) (citations omitted). As the Court noted in Terry, and as the district court suggested in its suppression ruling here, it “would have been poor police work” for an experienced officer to give up an investigation of suspicious behavior solely because that behavior might also have an innocent explanation. See Terry, 392 U.S. at 23, 88 S.Ct. 1868.
For that reason, a stop conducted in the face of ambiguity is permissible so long as it remains sufficiently probable that the observed conduct suggests unlawful activity. See Cortez, 449 U.S. at 418, 101 S.Ct. 690 (“The process does not deal with hard certainties, but with probabilities.”). The “relevant inquiry is not whether particular conduct is ‘innocent’ or ‘guilty,’ but the degree of suspicion that attaches to particular types of noncriminal acts.” United States v. Sokolow, 490 U.S. 1, 10, 109 S.Ct. 1581, 104 L.Ed.2d 1 (1989), quoting Illinois v. Gates, 462 U.S. 213, 243-44 n.13, 103 S.Ct. 2317, 76 L.Ed.2d 527 (1983).
By this reasoning, Officer Johnson would not have been justified in stopping the car here merely because it had a temporary registration tag that might have been phony. But after he and the dispatcher had both checked the relevant database and found no record of the car’s registration in Indiana, he had a reasonable suspicion that justified this stop. An officer need not be absolutely certain; without specifying mathematical probabilities, the degree of suspicion needed to justify a traffic stop is “considerably less than proof of wrongdoing by a preponderance of the evidence,” and “obviously less” than that needed for probable cause. See Sokolow, 490 U.S. at 7,109 S.Ct. 1581.
Officer Johnson had learned that the registration information on Miranda-Soto-longo’s car did not appear in the database specifically designed for the purpose of verifying that information. He had also observed that the registration tag could easily have been a home-made forgery. In his view, these facts, taken together, meant there was a distinct possibility that the car was either unregistered or stolen. We agree. Although it turned out that the car was neither, Officer Johnson had the reasonable suspicion needed to justify his *670initial detention of the defendant in the traffic stop.
That does not mean we would necessarily uphold such a stop on a different record. For example, as other courts have reasoned, if there were evidence that the database was unreliable because a large percentage of lawfully registered cars with temporary registration tags did not appear in the database, the inability to verify the registration information standing alone might not support a reasonable suspicion. See Mounts, 35 F.3d at 1213 n. 4 (absence of database information might not be sufficiently probative of unlawful activity if defendant “established that a large percentage of registered automobiles in Georgia did not appear on Georgia’s computer system”); Cortez-Galaviz, 495 F.3d at 1209 (demonstrating that a law enforcement “database is unreliable might well form a persuasive basis for a suppression motion”); United States v. Esquivel-Rios, 725 F.3d 1231, 1235-38 (10th Cir. 2013) (remanding for further proceedings on reliability of database in light of dispatcher’s comment that “Colorado [temporary] tags usually don’t return” in searches of database).
That is, it would be much harder for an officer to reasonably suspect wrongdoing if the sole basis for that suspicion were an unreliable database. Miranda-Sotolongo asserts a plausible theoretical basis for why the database might be unreliable when it comes to temporary tags — the delay between registering a ear and adding that new data to the database.' His failure to offer evidence supporting that theory means, however, that we cannot reverse on the speculative theory that this database was too unreliable to justify the stop. See Mounts, 35 F.3d at 1213 n.4; see also EsquiveURios, 725 F.3d at 1235 (distinguishing between evidence suggesting unreliability and mere assertions of unreliability); Cortez-Galaviz, 495 F.3d at 1209 (evidence that database was not reliable “might well form a persuasive basis for a suppression motion,” but argument required evidence rather than speculative possibility).
Miranda-Sotolongo argues in effect that the silence in the record should be held against the government rather than against him, citing United States v. Uribe, 709 F.3d 646 (7th Cir. 2013). There, the government attempted to justify a stop based on reasonable suspicion that the defendant had been driving a stolen car. The sole basis for that suspicion was that the registration database indicated a different color for the car. We doubted that an officer could reasonably infer that the col- or discrepancy was enough by itself to suggest car theft, and the government offered no evidence that it did. We concluded that the officer lacked reasonable suspicion to justify the stop. Id. at 652.
The reasoning of Uribe does not extend to the facts here. First, the inferential step needed to bridge the gap between the observed facts and unlawful conduct seems much shorter here than it was in Uribe. A color discrepancy between the real car and the database provides a much weaker basis for inferring the car is likely stolen or not properly registered than does a car’s complete absence from the database. Vehicle owners do not need the state’s permission to. repaint their cars. Second, unlike in Uribe, the government here offered evidence that the inference of unlawful conduct was supported by Officer Johnson’s experience. While the government might have strengthened its case for reasonable suspicion by providing some quantitative evidence about the correlation between finding no registration information in the law enforcement database and the car being either stolen or unregistered, see Ur-ibe, 709 F.3d at 652, we do not believe *671evidence of that sort was required to uphold this stop. See Mounts, 35 F.3d at 1213; Cortez-Galaviz, 495 F.3d at 1206.
The database here was not perfect, but few are. Nevertheless, the law’s usual presumption of correctness of such records justified reasonable suspicion, at least in 'the absence of evidence that Officer Johnson could not reasonably rely on the absence of a registration record to support an investigative stop. See Esquivel-Rios, 725 F.3d at 1235 (remanding denial of motion to suppress where defendant offered evidence that dispatcher told officer that database “usually” did not include current information about temporary tags from state in question). To justify suppression, Miranda-Sotolongo would have needed to offer evidence to undermine that presumption of correctness. He did not. The district court did not err by denying the motion to suppress.
II. Supervised, Release Conditions
Miranda-Sotolongo also challenges several special conditions of the supervised release term of his sentence, arguing that they are too vague and that the district court did not justify sufficiently its decision to impose them. Miranda-Sotolon-go had advance notice of these conditions (from the'presentence report) and did not object to these conditions in the district court. On the other hand, parties need not take “exceptions” to decisions a court has already made in order to challenge them on appeal. See generally United States v. Kappes, 782 F.3d 828, 843-44 (7th Cir. 2015) (discussing tension in our decisions about standard of review for conditions of supervised release for which defendant had advance notice and did not object or take “exception”).
While the district court here followed practices long accepted in this circuit, our more recent cases require that we vacate the four conditions and remand for reconsideration of them by the district court. One condition requires defendant to “refrain from excessive use of alcohol,” which we have treated as too vague. See, e.g., United States v. Baker, 755 F.3d 515, 524 (7th Cir. 2014), following United States v. Siegel, 753 F.3d 705, 715 (7th Cir. 2014). A second condition prohibits purchase, possession, use, distribution, or administration of “mood-altering substances,” which we have also treated as too vague. E.g., Siegel, 753 F.3d at 713, 715 (7th Cir. 2014). A third condition requires the defendant to undergo a program of substance abuse treatment involving no more than six tests per month to assess the use of alcohol and other illicit drugs. Per special condition 1, however, the appellant is permitted to consume alcohol, just not to excess. In Siegel, we described a similar condition as an “oddity” and suggested that it be clarified on remand. 753 F.3d at 716. The last special condition of supervised release requires Miranda-Sotolongo to “obtain his GED” within the first year of his supervised release term. We have recently vacated that condition while saying we would uphold a condition requiring a defendant to “seek” a GED. See United States v. Thompson, 777 F.3d 368, 381 (7th Cir. 2015).
We are confident that the district court on remand will consider whether to impose similar but more narrowly tailored conditions and, if so, will explain its decisions to the extent required by our more recent decisions that are by now familiar to all district judges in the circuit. See United States v. Farmer, 155 F.3d 849, 852 (7th Cir. 2014) (explaining that judges are required to “give a reason, consistent with the sentencing factors in section 3553(a), for every discretionary part of the sentence that the judge is imposing, including any non-mandatory conditions of super*672vised release”). Cf. United States v. Lewis, 823 F.3d 1075, 2016 WL 3004435 (7th Cir. 2016) (holding that defendant waived objections to sufficiency of district court’s explanation of reasons for supervised release conditions by declining invitation to raise issue). The problems here are narrow enough that we see no need to order a full re-sentencing.
Accordingly, the district court’s denial of the motion to suppress is AFFIRMED, and the challenged conditions of supervised release are VACATED, and the case is REMANDED for reconsideration of those conditions of supervised release.
. Delaware v. Prouse, 440 U.S. 648, 99 S.Ct. 1391, 59 L.Ed.2d 660 (1979), held that police could not stop motorists to conduct “spot checks” of registration information, including database checks of cars driving by, unless the officer had a specific reason to suspect the motorist was engaged in criminal activity. The reasoning of Prouse does not extend from stopping a motorist to "spot checks” of public records based on the registration tags that must be displayed on a vehicle for all the world to see. See id. at 661, 99 S.Ct. 1391.