Moving in together was a big step, but after seeing the building’s rooftop, which would be outfitted with a number of barbecues come spring, the couple conferred for only a few minutes before deciding that they wanted the apartment. But only if there wasn’t a broker’s fee.

“I feel like if you’ve lived in New York long enough you can figure out how to find a nice place that doesn’t charge a fee,” Ms. Godzik said.

“If there had been a broker’s fee here, we probably would have passed, on principle,” said Mr. Cheal, who works as a property manager for a residential real estate company in Manhattan, and had recently walked away from a well-priced apartment in Williamsburg after the broker told him the fee was a whopping 20 percent.

Not only was this apartment no-fee, but when they sat down to talk about how much money they would need to provide up front, the broker said the building was partnering with a new company, Obligo, that covered the cost of the security deposit for financially qualified tenants in exchange for a small monthly fee for the duration of the lease, in their case $15. (Through the company, they also authorized the landlord to charge up to the full deposit if there were damages to the apartment.) All they needed to put down was the first month’s rent of $3,000.

“We used the money we would have paid for a security deposit to furnish the apartment,” said Mr. Cheal, who was more than happy to leave behind his apartment and also his broken-down Ikea furniture — “college-kid-like junk” — on the curb in Bushwick.

The couple had been living in their apartment for about four months when it was announced in January that the L train wouldn’t be shutting down after all.