Cops and district attorneys have agreed on a new protocol allowing police to more quickly obtain warrants to draw blood from drivers who refuse to take breathalyzer tests. The new process should let police draw blood from suspected drunk drivers at least two hours faster than the current average of seven hours, the New York Times reports.

Under current rules, cops can only apply for a warrant to draw blood after a suspected drunk driver has refused a breath test in the field, and a second breath test in the stationhouse. The new agreement will let officers request a warrant as soon as a driver refuses to take a breath test the first time. Officers and district attorneys have not yet determined whether blood can be drawn at precincts and other locations instead of hospitals, and whether the job will be done by doctors working for police, first responders, or other parties.

The push for faster blood testing comes after two fatal accidents in which NYPD officers refused to take breathalyzers and didn't take blood tests for hours. In the case of officer Andrew Kelly — who reportedly reeked of alcohol and slurred his speech immediately after hitting and killing a woman in Brooklyn in September — it took police seven hours to obtain a warrant for a blood test. By the time Kelly took the test, he had no alcohol in his system. Meanwhile, a blood test taken more than five hours after detective Kevin Spellman struck a Bronx woman last month revealed that his blood alcohol level was still well above the legal limit at 0.21.

A lawyer who has represented several people arrested for drunk driving told the Times that the new process won't necessarily save much time. “Generally, they take you right to the precinct for the second test, and that is not that long after the person is arrested,” said attorney Howard Weiner. “In many states you don’t need a court order to take the blood. That would save a lot of time.”