The Chicago police chief has been fired, but that won’t solve Chicago’s or America’s problem with politics and policing. The investigation into the horrific killing of 17-year-old Laquan McDonald, shot 16 times by Officer Jason Van Dyke, went wrong because of politics. And just as the prosecution of Van Dyke will not change the police culture of contempt for black lives evident in the video recordings, the firing of Superintendent Garry McCarthy will not get the politics out of policing. Only independent investigation of these incidents can do that, and it is past time to put that in place in every state in the country.

The problem is not a lack of independence just from the police, but independence from city politics. Since 2007, Chicago has had an agency separate from the police to investigate officer-involved shootings, but the “independent” agency (the Independent Police Review Authority, or IPRA) is still under the mayor, and generally retreats from any investigation that might lead to criminal charges. Until we get investigations of cases like this out of the hands of politicians, even the best policies a police chief can impose won’t change the culture.

The good news is that other countries haunted by police violence have figured out how to do this. The problem isn’t fully solved anywhere, but we can make real progress, quickly building on what other countries divided by race, religion, and violent policing have learned.

When Nelson Mandela and the African National Congress negotiated a new constitution for post-apartheid South Africa, they insisted on an independent agency to investigate deaths at the hands of police. Mandela’s government launched the resulting Independent Police Complaints Directorate in 1997, with its own detectives to handle the criminal investigations and the discretion to investigate any complaints against police. This was the first permanent oversight body in the world established to conduct independent, criminal investigations of officer-involved shootings from the first hours to conclusion, breaking from the American pattern of civilian oversight bodies that routinely hand-off to others any investigations that might lead to criminal charges. Renamed the Independent Police Investigative Directorate (IPID) in 2011, the South African agency has struggled to fulfill its mandate, though just last month investigators of the IPID arrested four South African police officers and charged them with murder in the execution-style shooting death of an injured suspect.

Another divided society, Northern Ireland, followed South Africa’s example in 2000 with the creation of its police ombudsman, which conducts best-in-class criminal investigations of all police killings and many other cases of alleged misconduct. With authority to lead the evidence collection from start to finish, and a superb corps of detectives, the office established a stellar reputation under the first police ombudswoman, Nuala O’Loan.

Of course the United States is not South Africa or Northern Ireland, but the same powerful model has since been followed across all of England and Wales. There, the creation in 2004 of the Independent Police Complaints Commission (IPCC) has demonstrated that a permanent agency, independent of politics, can work in calmer societies as well, and can be institutionalized across a large state with multiple police departments. The IPCC in England also has its own detectives who conduct independent criminal investigations of police, including all deaths at the hands of police. Ever since its chairman won a battle with London’s Metropolitan Police over the right to conduct the criminal investigation into a tragically botched anti-terrorism operation in 2007, which ended with the police execution of a wholly innocent civilian, the IPCC has greatly increased police accountability in England and Wales, as well as increasing public confidence in that accountability.

Unlike these three examples, Chicago still follows the old model of civilian oversight common across the United States: a body that investigates allegations of some misconduct, but hands over criminal investigations in serious cases to other agencies. As the now-departed Superintendent McCarthy told the press last week, the investigation of the shooting death of Laquan McDonald “went from Chicago PD to IPRA, from IPRA to the State’s Attorney, FBI, and the U.S. Attorney.” Under the better model, an independent investigative agency would have responded to the crime scene and run the investigation straight through to the arrest of Officer Van Dyke (and perhaps others for what may have been a cover-up).

Earlier this year, Illinois became the first state in the country to adopt legislation implementing a series of the recommendations of the President’s Commission on Policing in the 21st Century, including a provision that is meant to insulate investigation of officer-involved shootings from the local politics where the shooting occurred. The legislation was crafted deliberately to allow Chicago to avoid shifting the way it investigates these cases under mayoral control. That special treatment should be eliminated and investigation free of politics made a reality across Illinois.

These investigations should become the province, from start to finish, of a new statewide Independent Police Investigative Commission replacing IPRA with authority to hand its results both to prosecutors and to the public. Indeed, every state should establish such an agency, and the federal government should provide training and financial support. As we head into the 2016 presidential election year, with Illinois’s legislature and governor already demonstrating leadership, it’s a worthy and achievable goal.