Angeliesse and Mike Nesterwitz met and married as New York Police Department officers.

They each made more than $100,000 a year, but life had become unbearable. The couple were eager to start a family, but they barely saw each other because they were constantly pulled into mandatory overtime shifts. Mr. Nesterwitz would often finish a tour and sign out only to learn that he had to sign right back in again.

“We were going to get a house, thinking, ‘Are we even going to enjoy that house?’” he said. “I want to work to live, not live to work.”

In 2022, they left for Florida.

Their story illustrates a larger problem at the Police Department, where officers have been leaving in droves and leaders are leaning hard on overtime to make up the shortfalls.

It’s a strategy that in the 2024 fiscal year cost the department more than $1 billion, twice what it had budgeted for overtime, and created opportunities for corruption, capped by the resignation of Jeffrey Maddrey, the top uniformed officer. He came under investigation after a lieutenant accused him of coercing her into sex in exchange for hundreds of thousands of dollars in overtime.

To solve the problem, Commissioner Jessica S. Tisch has been cracking down on the hours, even as thousands of officers may respond by retiring to avoid seeing their pensions shrink. The recruitment picture is just as bleak, with the number of people signing up to take the entrance exam plunging by more than half since 2017.

“I am not going to sugarcoat the real recruitment issues that we’re facing,” Commissioner Tisch said on Thursday during a speech before the New York City Police Foundation and department brass. “N.Y.P.D. applicants used to wait for years to get the call to join the academy. Now we are practically begging people to take the exam.”