Go ahead and pop the champagne: the NYPD will no longer arrest most people who are caught drinking alcohol in public in Manhattan, the city announced today—but they can still get a summons.

Unless it’s “necessary for public safety reasons,” the NYPD will no longer arrest people for certain low-level offenses in Manhattan, including public consumption of alcohol, public urination, littering and riding between subway cars or taking up more than one subway seat—and Manhattan District Attorney Cyrus Vance Jr. will no longer prosecute those infractions, his office said today. Offenders can still receive summonses, which require them to pay a fine but don’t give them a criminal record, for those offenses. Summonses are already an option for this offenses, and are often given to violators who do not have a warrant.

“Using summonses instead of arrests for low-level offenses is an intuitive and modern solution that will help make sure resources are focused on our main priority: addressing threats to public safety,” Mayor Bill de Blasio said in a statement. “Today’s reforms allow our hardworking police officers to concentrate their efforts on the narrow group of individuals driving violent crime in New York City. This plan will also help safely prevent unnecessary jail time for low-level offenses.”

But Mr. de Blasio’s office did not put out a press release about the topic, nor did the NYPD. Instead, it came only from Mr. Vance’s office—meaning it likely missed the mailbox of many in the political press corps. The DA touted it as an announcement from him, Mr. de Blasio, and Police Commissioner Bill Bratton, but there was no press conference. Mr. Vance was out of state today testifying to Congress, according to his public schedule.

The announcement follows a call from Council Speaker Melissa Mark-Viverito to use summonses instead of arrests for low-level crimes citywide. The news announced today applies only to Manhattan, and this specific initiative began with Mr. Vance, his office said—hence why it doesn’t apply elsewhere.

“By ensuring courts are not unnecessarily bogged down with minor offenses committed by those who pose no threat to public safety, we help focus police and prosecutorial resources on those who commit serious crimes,” Mr. Vance said. “By giving cops the discretion to issue summonses instead of requiring them to make arrests, we ensure they do not spend hours processing cases as minor as littering, and we enable officers to get back to patrolling, investigating, and keeping our neighborhoods safe.”

But some people who are stopped for these minor offenses may still end up in handcuffs—if they have warrants out for their arrest when they are stopped, they’ll be arrested on that warrant.

In fact, many of the people who were previously arrested for these kinds of low-level crimes, rather than getting a summons, were arrested because of an outstanding warrant—but they were often arrested for the new offense, adding another arrest to their record. That will no longer be the case, the DAs office said. If someone has a felony warrant for a crime like burglary, and they are stopped for an open container, they’ll be taken to jail on the warrant, but will only get a summons for the open container violation.

And if someone has an open summons warrant—let’s say they didn’t pay their summons the last time they got caught littering and then they get stopped for that again—they’ll be “detained,” according to the DA’s office, and brought to court to face a judge on that summonses and the new one. But they won’t be arrested.

Ms. Mark-Viverito has argued that old warrants themselves are bogging down the criminal justice system, and in her State of the City called for wiping out more than 700,000 of them in the city, for low-level crimes like the ones Mr. Vance will stop prosecuting.

A single borough changing its approach to prosecuting certain crimes is not without precedent. In 2014, Brooklyn District Attorney Kenneth Thompson announced he would no longer prosecute low-level marijuana crimes. Later, the city adopted a similar policy—ordering cops to issue summonses rather than arrests for possession of small amounts of pot.

The policy change will begin March 7. Mr. Vance’s office estimates the changes will mean about 10,000 fewer arrests each year on low-level offenses.