Finding an apartment in New York that does not drain your bank account can feel like a nearly impossible task.

Competition is fierce. And for what? Cramped spaces that deliver little more than a grinding commute to work. But knowing where to look — and when to act — can mean the difference between crummy or cozy quarters. Apartments for less than $1,500 a month do exist, as long as you’re willing to take on a roommate or two or explore neighborhoods that might be less than convenient to your work. Price, of course, dictates most searches. Pay too much and a tight budget can spiral into an unmanageable one. More than half of all New Yorkers are considered “cost burdened,” meaning they spend more than a third of their income on rent.

As the city’s population grows, the number of apartments available shrinks, particularly the cheaper ones. The median income for New Yorkers in 2015 was $56,350 a year, which puts median housing costs at $1,409 a month for rent and utilities, according to the New York University Furman Center. Yet in May, the median rent for a Manhattan apartment was $3,475 a month, according to a Douglas Elliman report. To pay that much without being burdened, you’d have to earn $139,000 a year.

“Rents have gone up, there’s no doubt about that,” said Vicki Been, the faculty director at the Furman Center and a former commissioner of the city’s Department of Housing Preservation and Development. “At the same time, people’s incomes have stayed flat. That’s making housing less affordable.”

And what about recent college graduates moving to New York in search of jobs and housing? While someone starting out in finance is looking at a median starting salary of $70,000 a year, jobs in arts and entertainment, for example, offer a much smaller starting median wage of $29,700 a year, according to data provided by the job site GlassDoor.com. Do the math, and many New Yorkers should be paying considerably less than $1,000 a month in rent.

To find those apartments, renters “are going to have to look long and hard,” Ms. Been said. “People are having to make trade-offs. The cheaper the apartment, the further away from transit it is.”

Know Where to Look

The search for apartments fitting a smaller budget often leads to pockets of the city that are rapidly changing, but often lack conveniences like express trains, shops and restaurants. Although rents have been stagnating over the last two years, they are still near historic highs. And neighborhoods that were considered reasonably priced options just a few years ago no longer are.

“We used to do studios in East Harlem all the time,” said Shawn Hindes, a founder of Teacher Space, a brokerage firm that helps new teachers find apartments. “But that’s not really feasible anymore on a teacher’s salary.” The same goes for many Brooklyn neighborhoods. “Five years ago, someone saying ‘I want a place in Crown Heights’ got the pick of the litter,” he said. But that is no longer the case.

In 2016, only about 14 percent of the one-bedroom apartments listed in Crown Heights on StreetEasy were asking less than $1,500-a-month rent; and in Washington Heights, around 10 percent of one-bedrooms asked less than $1,500 a month, according to data provided by StreetEasy.

But head over to a Brooklyn neighborhood like Northeast Flatbush, an area south of Crown Heights, and about 63 percent of the one-bedrooms were listed for less than $1,500 a month last year; while in Norwood in the northwest Bronx, almost 94 percent of them were, according to StreetEasy.

“These are predominantly residential neighborhoods with older housing stock,” said Grant Long, the senior economist for StreetEasy.

Mr. Hindes of Teacher Space said young teachers who once might have looked in East Harlem are now heading to neighborhoods like Morris Heights in the West Bronx. In Brooklyn, neighborhoods like Flatbush, Prospect-Lefferts Gardens and Kensington are getting more traffic, according to Harley Courts, the chief executive of Nooklyn, a brokerage firm that also helps renters find roommates. “Half of our inventory has shifted south in the last 18 months,” deeper into Brooklyn, Mr. Courts said.