The next spring, Mr. Tueller published his findings in SWAT magazine and transformed police training in the United States. The “21-foot rule” became dogma. It has been taught in police academies around the country, accepted by courts and cited by officers to justify countless shootings, including recent high-profile episodes involving a homeless woodcarver in Seattle and a schizophrenic woman in San Francisco.

Now, amid the largest national debate over policing since the 1991 beating of Rodney King in Los Angeles, a small but vocal number of law enforcement officials are calling for a rethinking of the 21-foot rule and other axioms that have emphasized how to use force, not how to avoid it. Several big-city police departments are already re-examining when officers should chase people or draw their guns and when they should back away, wait or try to defuse the situation.

“In a democratic society, people have a say in how they are policed, and people are saying that they are not satisfied with how things are going,” said Sean Whent, the police chief in Oakland, Calif. The city has a troubled history of police abuse and misconduct, but some policy changes and a new approach to training have led to sharp declines in the use of force, Chief Whent added.