EASTERBROOK, Circuit Judge.

According to a dispatch based on a 911 call, a black man driving a maroon car had pulled a gun near 103rd Street and Pulaski Avenue in Chicago. Police arrived swiftly and found Leonard Askew’s maroon car on the median that divides Pulaski’s lanes. They asked Askew, who is black, whether he had a gun; he said no, though a frisk turned up a knife. Craig Padgett and Carrie Lis, who had been standing at the side of the road, told the officers that during a road-rage incident Askew had brandished a knife and threatened to kill them. (Padgett accused Askew of hitting Lis’s car, and an argument ensued.)

Officers Frank Quinn and Walter Pu-chalski took Askew into custody and charged him with making an armed threat, placing Padgett and Lis in apprehension of battery. He was released on bond the next morning. Charges were dismissed when Padgett and Lis failed to appear in court. Askew then sued Quinn and Pu-chalski under 42 U.S.C. § 1983. He contends that they violated his rights under the fourth amendment by arresting him without probable cause. (Askew also seeks to hold the City of Chicago liable on state-law theories that we need not discuss.) The district court granted summary judgment for the defendants. 2005 U.S. Dist. Lexis 8276 (N.D.Ill. Apr. 6, 2005).

Gramenos v. Jewel Companies, Inc., 797 F.2d 432 (7th Cir.1986), holds that allegations by eyewitnesses supply probable cause when the statements, if true, show that a crime has occurred. It does not matter, Gramenos adds, whether the accused person denies the allegations. Police need not conduct an investigation but may arrest and let prosecutors and courts determine who is telling the truth. See also, e.g., Wilson v. McRae’s, Inc., 413 F.3d 692 (7th Cir.2005); Driebel v. Milwaukee, 298 F.3d 622, 643-44 (7th Cir.2002); Pasiewicz v. Lake County Forest Preserve District, 270 F.3d 520, 524 (7th Cir.2001).

The Gramenos principle has qualifications: when, for example, the police know that the accuser may harbor a grudge against the accused, see Hebron v. Touhy, 18 F.3d 421 (7th Cir.1994) (dictum) (evicted tenants’ accusations against landlord), or when it is doubtful that the allegations (even if true) add up to a crime, see BeVier v. Hucal, 806 F.2d 123 (7th Cir.1986), then some follow-up may be required to make an arrest “reasonable.” The police did not have any reason to suspect that Padgett and Lis were out to frame Askew, however, and a threat to kill or maim regularly is dealt with by criminal prosecution. Askew was armed with a knife, and his car was stopped in the middle of a thoroughfare, itself an offense and a potential reason for arrest. See Whren v. United States, 517 U.S. 806, 116 S.Ct. 1769, 135 L.Ed.2d 89 (1996); Atwater v. Lago Vista, 532 U.S. *896 318, 121 S.Ct. 1536, 149 L.Ed.2d 549 (2001).

Recognizing that the story Padgett and Lis told, if taken at face value, establishes probable cause for arrest, Askew wants a crack at arguing to a jury that the officers should not have believed his accusers. There was a discrepancy between the radio dispatch (that the assailant had a gun) and the statements at the scene (that the assailant had a knife). If Padgett and Lis changed their stories, perhaps they were making it all up — though perhaps the dispatcher heard Lis wrong on the phone or misspoke on the radio. Askew adds that Padgett and Lis acted suspiciously by inquiring whether they would be compelled to appear in court and what would happen to them if they did not. Askew takes that as evidence that they were bringing false charges, though perhaps the police thought it implied their fear of Askew and a desire to disappear from his life as quickly as possible. Finally, Askew sees it as suspicious that Padgett and Lis signed the criminal complaint before the officers completed it (a task they did not finish until reaching the stationhouse); were they anxious to avoid a perjury rap? Only a jury can sort out these inconsistencies, Askew maintains.

If these subjects were material, then there would be work for a jury to do. They are not material. Padgett and Lis said that they had been threatened by a man with a weapon, and a search revealed that Askew (whose maroon car was just where the 911 call placed the incident) had a weapon. It is possible, we suppose, that Padgett and Lis were trying to get someone — anyone—in trouble and were surprised when an innocent person happened to be carrying a knife, and then quickly changed their story from gun to knife, but this is unlikely. Why would mischief-makers hang around, waiting to be caught and prosecuted themselves? A slip of the tongue (whether by Lis during the call or by the dispatcher) is much more likely. Defendants suggest another possibility: perhaps someone else saw the altercation and made an independent 911 call, describing the weapon incorrectly. Askew could have cleared this up by obtaining a recording of the 911 call. He did not do so.

The idea behind Gramenos and similar decisions is that police often encounter competing and inconsistent stories. One person makes an accusation; another denies it; police on the scene must act yet lack the tools to determine immediately where the truth lies. The Constitution permits them to initiate the criminal process and leave the sifting of competing claims and inferences to detectives, prosecutors, judges, and juries in the criminal prosecution. If states think that this gives accused persons insufficient protection, they are free to enact statutes either staying the officers’ hand or providing recompense to those exonerated in the criminal process.

The sort of inconsistencies to which Askew points are normal. Eyewitnesses remember things differently. Police don’t always follow correct procedure (here, defendants concede, they should have completed the charge form before the complaining witnesses signed). If these were sufficient to permit second-guessing and damages, then the job of policing would be very risky financially as well as physically. Police would respond by disbelieving witnesses (or not acting on allegations), lest they end up paying damages, and the public would suffer as law enforcement declined. Often the victims themselves live in the shadows and do not fancy a trip to court, which may expose aspects of their lives they prefer to keep hidden; arresting on their accusations would be especially risky to the police; yet everyone is entitled to protection from crime, and that protec *897 tion would erode if the arrested person could collect from the police every time a civil jury concludes that it would have handled the incident differently. That’s why we have held that the sort of inconsistencies and glitches that characterize real investigations do not disentitle police to rely on eyewitness statements. See, e.g., Spiegel v. Cortese, 196 F.3d 717, 724-26 (7th Cir.2000); Gerald M. v. Conneely, 858 F.2d 378, 381 (7th Cir.1988).

It is uncontested that Padgett and Lis, in view of Askew, identified him as their assailant. He was found with a knife, which Padgett and Lis identified as the weapon that Askew had brandished. His car was stopped in the median of a busy street, a position consistent with a road-rage altercation. These uncontested facts supply probable cause for his arrest.

Affirmed