IN THE basement of St Gregory’s church in Crown Heights, a Brooklyn neighbourhood where kosher pizzerias compete with jerk-chicken shacks for business, the officers of the 77th precinct are giving away colouring books for children. “Police officers are your friends,” the book’s title proclaims. Around the city, protests at the decision not to prosecute the officer who choked Eric Garner to death suggested that plenty of New Yorkers did not agree.

A few blocks away, not long after the precinct’s black commanding officer listened to complaints of police racism from 100 mostly black residents of the neighbourhood, a mentally disturbed man with a knife stabbed an Israeli student at an Orthodox religious school. Police shot the knifeman dead, after he threatened to stab more people, to the relief of some of the assembled faithful. The police were their friends after all.

If it is to work well, the relationship between police and policed requires mutual trust. “Public safety without public approval is not public safety,” says Bill Bratton, New York’s police commissioner. After Mr Garner’s death, which was captured on camera, complete with his last words (“I can’t breathe”, gasped ten times or so), and the shooting by a policeman of Michael Brown in Ferguson, Missouri, in August, public approval is in short supply.

Both cases involved white officers killing unarmed black men, and neither of the officers has been indicted for wrongdoing. The two cases are not the same, however. Mr Garner was selling loose, untaxed cigarettes in the street and posing no threat to anyone. Mr Brown’s case is murkier, since there is no video footage. A friend of Mr Brown’s, with him when he robbed a convenience store shortly beforehand, says that the policeman shot him in cold blood. The policeman says he acted in self-defence, after the 292lb Mr Brown attacked him and tried to grab his gun. The forensic evidence tends to support the officer. Public opinion divides along racial lines. Nearly all African-Americans think the failure to indict the officers involved was wrong in both cases. Whites make a distinction: 64% think the grand jury made the right decision in Mr Brown’s case but only 28% think that about Mr Garner’s, according to a Pew poll. The FBI counts over 400 “justifiable homicides” by American police officers every year. This number includes only those shot while committing a crime. Reporting such shootings is voluntary, so the true number is surely higher. Even undercounting, America easily outguns other rich countries: in the year to March 2013 police in England and Wales fired weapons three times and killed no one. Such comparisons should be read in context. America’s police operate in a country with 300m guns and a murder rate six times Germany’s. In recent years the New York Police Department (NYPD) was called to an annual average of almost 200,000 incidents involving weapons, shot 28 people and saw six of its officers shot (mostly non-fatally). Despite the headlines, it is one of America’s more restrained forces.

The more trigger-happy police departments tend to be found in smaller cities where fewer journalists live. Peter Moskos of John Jay College has come up with a measure to identify them, which checks the number of police shootings against the number of murders in a city. The places that stand out as having a lot of police shootings relative to the number of murders are Riverside, San Diego and Sacramento in California; and Tucson and Phoenix in Arizona.

In general, smaller police forces are less likely to have proper oversight. (This matters: half of America’s 12,500 local police forces have ten or fewer officers.) Larger jurisdictions can employ people whose job is to prosecute policemen. In Brooklyn (population 2.5m), the current district attorney made his name prosecuting an officer for sodomising a handcuffed Haitian immigrant with a broomstick in the lavatory of a police station. In a small town policemen are investigated by people they work with all the time. “The prosecutor is the guy who went to your kid’s confirmation,” says Mr Moskos. In the whole country, fewer than six officers were charged with murder or manslaughter each year, on average, between 2005 and 2011, according to Philip Stinson of Bowling Green State University.

If the problem were just one of scale then the answer would be simple, at least in theory: merge small departments to form bigger ones. But even in some fairly large cities some officers are too eager to use force. When a police force has been the subject of frequent complaints, the Department of Justice (DoJ) is often called in to investigate and make recommendations.

Under Barack Obama’s administration, the department currently has 27 active cases, looking at city forces such as Seattle’s or Cleveland’s and also at some individual sheriffs’ departments. Though the DoJ finds that, even in the worst departments, most shootings are justified, they also show that the shooting of unarmed people who pose no threat is disturbingly common.

The body count in Albuquerque

Albuquerque, New Mexico, is a strong contender for the country’s most violent force. In 2009, according to the DoJ, one of its officers pulled a man over for driving with no rear lights. The driver, Andrew Lopez, ran away. One of the officers chasing him thought Mr Lopez had “the biggest handgun that he had ever seen”, says a DoJ report, though he was in fact unarmed. The cop shot him three times and, as he lay wounded, shot him again in the chest, killing him. In 2011, when the case came to a civil trial, a police training officer called the officer’s actions “exemplary” and said he “would use this incident to train officers on the proper use of deadly force”.

A year later the city’s officers were called to an incident in which Kenneth Ellis, a 25-year-old army veteran suffering from post-traumatic stress disorder, had a gun to his head and was threatening to kill himself. An officer prevented Ellis’s suicide by shooting him in the neck, fatally. Another potential suicide poured petrol on himself: Albuquerque police tasered him, not realising that this would set him alight.

Violence against people who are in the midst of a mental crisis is a common theme of the DoJ’s reports. A 2011 investigation of Seattle’s police department turned up a case of a man whom police had found in the street, “yelling at traffic lights while holding a stuffed animal”. An officer ordered him to move to the side of the road and, when the man disobeyed, pepper-sprayed him. When the man made a fist, the officer hit him with a baton. When he ran, four officers chased him and punched him several times, kneed him, elbowed him and hit him again with their batons. He was then arrested on charges of pedestrian interference and obstruction.

Using violence to enforce footling laws is also a common theme. Mr Garner died while being arrested for selling single cigarettes on which he had not paid the full New York duty, which is so high that 76% of the cigarettes smoked in the city are bootlegged. Letitia James, New York’s public advocate, partly blames the “broken windows” theory of policing for Mr Garner’s death. This theory holds that police should use statistical models to identify areas where crime is likely to happen and then flood them with officers who crack down even on minor offences in the hope of preventing more serious ones. It is widely considered a colossal success.

A more obvious culprit is the way policework is measured. Police managers fret about lazy officers. To keep them away from the doughnuts, most forces judge officers by how many arrests they make. Preventing a rape does not count; busting someone for jaywalking does.

There is a paradox in all this. American cities have become much safer in the past two decades. Too many urban forces do not seem to have noticed. In Cleveland, the DoJ found a sign in a police parking lot that read “Forward Operating Base”, as if it were an outpost in Afghanistan.

This is an unhelpful mindset. In 2012 a car containing Timothy Russell and Malissa Williams drove past the city’s police headquarters. Officers thought they heard a shot from the car and gave chase, though in fact neither the driver nor the passenger was armed. At least 60 police vehicles and over 100 officers joined in. The chase ended in a school car park, where 13 cops fired 137 shots at the car, killing its occupants. “The officers…reported believing that they were being fired at by the suspects,” said the DoJ. “It now appears that those shots were being fired by fellow officers.”

The federal government stokes the culture of the warrior cop by offloading surplus military kit to local police. The Los Angeles School District Police Department has acquired three grenade-launchers and a mine-resistant armoured vehicle, perhaps to keep its sophomores in check.

Sacking the bullies

Yet there are examples of police forces that have reformed. The Los Angeles police department made its police less like an occupying army after the riots that followed the beating of Rodney King in 1991, which like Mr Garner’s choking was filmed by a bystander. New York’s department did something similar, banning officers from firing shots as warnings, from shooting at vehicles or from firing unless they thought a life was in danger. The number of shots fired by police in New York has fallen by more than two-thirds since 1995.

In both cities the police are now blacker than the populations they serve—the opposite of Ferguson, Missouri. New York has begun a pilot programme under which officers will wear body cameras. The recordings will be used to deter bad behaviour both by police and by the public; to provide evidence after violent encounters; and to protect officers against baseless complaints.

Even with these changes, “There is at least one crazy cop in every precinct,” says a retired NYPD officer. Everyone else knows who they are, but they are impossible to sack until they do something really stupid. The officer who choked Mr Garner had been sued for wrongful arrest, and was accused of ordering two black men to strip naked in the street for a search. (He denied it, and one case was settled.) Reformers think the procedure for sacking bullies in uniform should be much swifter. Those who enforce the law should also obey it.