Twenty years ago, the reputation of the New Orleans Police Department was in tatters. Officers had opened fire on a group of civilians leaving the city after Hurricane Katrina, and then tried to cover it up.

They killed other people with impunity, a Justice Department investigation found. They forgot to lift fingerprints at homicide scenes. Police dogs attacked their handlers.

Today, the department’s stature has vastly improved, even in the eyes of some of its most stringent critics. “I have seen dramatic improvements in many aspects of N.O.P.D.’s handling of misconduct,” said William Most, a civil rights lawyer who regularly represents clients who are suing the police.

Mr. Most attributes the improvement to a consent decree, an agreement that has kept the department under strict federal oversight for more than a decade. Such agreements are rarely used but can bring extensive change. They are the federal government’s most powerful tool to overhaul troubled departments, and they set a de facto standard for American policing.

But they also have critics, who say that the agreements are written with little regard for their practical effects, and that they go beyond correcting unconstitutional behavior to impose a progressive vision of policing.

On Wednesday, the Trump administration, which has been critical of consent decrees, announced that it was dropping the consent decree process in eight jurisdictions. The moves dashed the hopes of residents who saw federal intervention as their best hope of forcing change, but pleased those who saw the agreements as too broad, too restrictive of the police and too ideological.