Earl Wilson/The New York Times

Sarah Stevenson scampered through a heavy rain one recent Friday evening, arriving at a Manhattan rental agency just before it closed.

Ms. Stevenson, a 26-year-old nurse’s aide from Brooklyn, had reserved a compact cutie with a lot of spunk for tooling around on the weekend.

The man behind the counter went and fetched it from a pillow in another room.

“Hi, hi, hi,” Ms. Stevenson said with a smile that kept getting wider. “How have you been, my handsome boy? I missed you.”

Ms. Stevenson picked up Oliver, a 3-year-old cockapoo — half cocker spaniel, half poodle — whom she had rented before.

“Last weekend, I didn’t want to bring him back because we were having the best time,” she said as she ran her fingers through Oliver’s tan curly locks.

The agency was Flexpetz, which rents dogs that have been rescued from animal shelters in the hope that they will eventually be adopted. Flexpetz operates out of the Wet Nose Doggy Gym at 34 East 13th Street, which provides day care and boarding for dogs. The company started in San Diego and opened in Los Angeles in June and in New York in October. It plans to expand to Boston, Washington, San Francisco and London.

“There are a lot of people out there looking for companionship,” said Chris Haddix, 28, who runs the New York branch of Flexpetz. There are usually five or six dogs available for rent, many of them on display in the Wet Nose storefront window, attracting crowds.

Ms. Stevenson explained why she was a customer: “I’m single and moved here from Scotland two years ago, and it’s been difficult to meet people because everyone in New York just kind of goes about their business. But when I’m walking around with Oliver, I seem to get into so many conversations about him. It becomes a nice way to meet people.”

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