Keeping the population of stray cats in check requires a systematic approach, animal advocates say: To ensure that every cat in a colony has been sterilized, caretakers get to know their wards so that they can better monitor the size of the population. Under their watchful gaze, any new cats who wander in can be separated and taken to a veterinarian. The cats have the top of their left ears clipped as a sign that they have been neutered.

Not all cats are as hard to trap as Tom Waits, who earned his name because his rough exterior recalled the gruffness of the singer’s voice. Usually, caretakers withhold food for a few days before luring hungry cats into baited cages with drop doors.

When she moved to Bushwick, Brooklyn, last August, Myra McMinn, 32, noticed several cats that would meander through her backyard, so she put cat food out from time to time. And then they multiplied.

All of a sudden, she said, “The seven cats had had nine kittens, and I did not know what to do.”

She sought answers online and found a group called Neighborhood Cats that offers workshops in trap, neuter and return. After attending a three-hour class, Ms. McMinn took a week off from a temporary job she has while getting a master’s degree at Columbia. She borrowed 19 cages and set about luring the cats with Fancy Feast. (The shyer ones required sardines.) With the help of a handful of volunteers, she caught 12 the first night.

“It was like camping and being a new mom,” Ms. McMinn said of the long night before the American Society for the Prevention of Cruelty to Animals showed up to take the cats to be neutered. “All the cats would yowl if one of the other ones pooped, so I was waking up every 10 to 30 minutes.”

The newly neutered felines were all returned to her; she had to let them recover for a few days in her room before they could go back outside. Now the cats come and go from the backyard but without any new kittens in tow.