By Jim Williams

CHICAGO (CBS) — PAWS Chicago needs you to take little furry, four-legged new friends home…as soon as possible.

It doesn’t happen very often, but the shelter is at capacity and desperately needs the room to save even more animals.

CBS 2’s Jim Williams has the story from the PAWS adoption center in Lincoln Park.

PAWS Chicago has created a national model for no-kill shelters. People who rescue cats and dogs want bring them here.

Right now, there’s no room.

It could be a while before this happens again: boxes of kittens arriving at PAWS Chicago’s Medical Center in Little Village.

If people call to bring over dogs and cats, Stacy Price said now is not a good time.

“Right now if we’re at capacity, we have to tell them no,” said Price.

A sad “no” here and at the PAWS Chicago Adoption Center in Lincoln Park.

“So we just have a lot of need and not enough space,” said Price.

PAWS Chicago could be a victim of its own success.

Its national reputation has grown for its humane care and for not euthanizing the animals, no matter how long they’ve been here.

Take Tyson, a six-year old lab mix with diabetes. He’s still waiting for adoption.

“His temperament is absolutely wonderful. The volunteers love him,” said PAWS’ Joan Harris.

PAWS Chicago said an increasing number of animal rescue organizations bring dogs and cats here, especially after natural disasters. Last year, hurricanes Harvey, Irma, Jose and Maria displaced pets.

“As soon as an animal leaves their suite room or cage, we fill it up with another room,” said Price.

So if six-year-old Tyson finds a home….

“We’re saving the lives of many, many other dogs,” said Harris.

This Saturday and Sunday, if you take in an older cat or dog like Tyson, PAWS Chicago will waive the fees.