After a decade-long spending spree and a devastating pandemic, New York City is now staring at three years of huge budget deficits, beginning with at least $4.2 billion in the year that starts in July of next year.

Mayor Eric Adams, rightly, is trying to wring some savings from the city’s $106 billion budget. But so far, he appears to be making some strange choices.

Among the most mystifying is a decision to shrivel the city’s free prekindergarten initiative by proposing a $567 million funding cut to the program and stopping its planned expansion. There are signs that the program is in need of attention: It has about 30,000 unfilled seats. The city also owes prekindergarten providers hundreds of millions of dollars in back pay, as Bloomberg reported on May 15, leaving many of them struggling to stay afloat. But rather than cut, New York City should increase its outreach and pay providers what they are owed. Poverty is on the rise in New York. This is no time to slash funding to a program that provides early education to 90,000 children across the city and could serve tens of thousands more.

Also on the chopping block in the mayor’s budget proposal: $5 million for a program that delivers meals for city seniors and $17 million for contractors that provide therapy, job placement and other social services for people in city jails. Frank Dwyer, a spokesman for the Department of Correction, said in a statement that the agency would provide the social services previously performed by contractors. But that could be difficult at the city’s jail complexes, which continue to suffer from violence and inmate deaths.

The cuts to these vital programs are part of an across-the-board search for savings through a 4 percent cut for nearly every city agency ordered by the mayor in April. In the 2024 fiscal year budget, which must be approved by June 30, the impact of many of those cuts on everyday New Yorkers might be relatively small. But with the deficit expected to increase to at least $6 billion in fiscal year 2026 and at least $7 billion in 2027, Mr. Adams will need a more targeted approach. Executing blanket cuts across city agencies in the coming years is almost certain to reduce core services for New Yorkers who need them the most.

A better way would be for the Adams administration to hunt more carefully for savings that have as little impact on residents as possible, ending programs that aren’t working while continuing to invest heavily in areas like housing and in programs that help vulnerable New Yorkers.

“It takes sleeves-rolled-up work,” Andrew Rein, the president of the Citizens Budget Commission, a nonpartisan budget watchdog group, told The Times. The City Council, which must approve the budget, has challenged the mayor’s budget cuts; its willingness to do so is a good thing.

Some city agencies that serve New Yorkers in poverty are severely understaffed and urgently need more investment. At one such agency, the Human Resources Administration, wait times for food stamps and other benefits are now often monthslong.

So what can be cut? One area for possible savings is reducing overtime worked by the city’s uniformed employees. New York City spent $1.56 billion on such overtime last year, according to a report from Comptroller Brad Lander. The New York Police Department accounted for $671 million, or 43 percent of that overtime.

The Citizens Budget Commission has suggested slashing administrative costs by consolidating the dozens of the city’s union welfare benefit and annuity funds.

The city’s Independent Budget Office has additional ideas, like ending $75 million in rental assistance to charter schools and increasing revenue by creating a civilian complaint program for vehicles that violate bike lanes. It also recommended hiring more tax auditors at the Department of Finance, a change the group said could add $165 million in revenue to the city’s budget every year.

Reports by New York’s budget watchdogs suggest the city’s economic outlook, while far from dire, is unsteady. As the nation heads into an uncertain economy, revenues in New York City are projected to continue to grow, but modestly. The city faces roughly $16 billion in costs from labor settlements in the coming years, and the mayor says it will have to spend at least $4.3 billion in the coming year alone to serve tens of thousands of migrants who have arrived from the southern border, though the Independent Budget Office says those costs are likely to be much lower. The $13.5 billion in federal stimulus aid that helped cushion the municipal budget during the pandemic is mostly gone.

Mr. Adams has asked for help from the White House to cover the costs of housing and settling those migrants. He’s right: Those costs should be covered by the federal government rather than borne by taxpayers in New York City or localities anywhere in the United States where members of this high-need population happen to settle. Hopefully, Gov. Kathy Hochul can help Mr. Adams make that case.

Pruning New York City’s nation-state-size budget is good fiscal policy. How Mr. Adams makes those cuts matters.