A poster greets owners surrendering their pets at Miami-Dade Animal Services’ shelter:

“We work tirelessly to save as many pets abandoned at Animal Services as possible...But last year, 3,558 of 5,182 kittens (68%), 8,267 of 9,233 cats (90%), 1,139 of 5,166 puppies (22%) and 7,072 of 16,300 dogs (43%) were euthanized because there were not enough homes for them. Please make sure you have exhausted all other options before leaving a pet at Animal Services.’’

But most people who hand over cats and dogs at the Medley shelter haven’t sought other options, much less exhausted them, and neither the stark statistics or frank talk from shelter personnel make much difference.

Gloria Acevedo brought 4-year-old Ariel, the mixed terrier she’s had since puppyhood, to the receiving room of Animal Services one day in September.

The dog had “mental problems,’’ she said. “She goes in the street. She almost bit a little boy.’’

Wagging her tail, Ariel stared expectantly up at Acevedo, who began to cry.

“I hope someone adopts her,’’ said Acevedo, of Homestead.

Leo Romero, animal care specialist supervisor, knows that’s unlikely. Ariel is no beauty. She’s had several litters and lost some teeth when she was hit by a car.

He tried to persuade Acevedo to reconsider, suggesting that if Ariel were spayed, she’d calm down — and if she stayed at the shelter, she’d probably die.

“We can do [the spaying] here for $30,’’ he said. “She’s a good dog and she’s very attached to you.’’

Acevedo brightened.

“OK, I’m gonna do that!’’ she said. But her husband wanted none of it.

“I’m not driving back up here,’’ said Jose Ramos. “You can’t keep her.’’

They headed for the door, leaving Ariel behind.

In came Isabel Fuentes and her 7-year-old-son Renato, with the brown puppy they’d gotten from Animal Services just days earlier.

“We live in an apartment,’’ Fuentes said, as her reason for returning the dog. And he was throwing up, Renato added.

Shelter personnel have heard every reason and every excuse in the receiving room: “I’m moving to a place that doesn’t accept animals.’’ “I lost my job.’’ “My kids are allergic.’’ “We changed the decor and the dog doesn’t match.’’ “It pees in the house.’’ “It scratches the furniture.’’

“I had a lady yesterday who brought in a dog because it had worms,’’ an easily treatable problem, Romero said. “I gave her a packet of dewormer.’’

People even give up their pets because they get fleas, he said, “but mostly, they just don’t want to deal with it anymore.’’

By the next day, the puppy, renamed Miles by the shelter staff, went home with a new family.

Nine days after the Homestead couple dropped her off, Ariel became one of some 20,000 animals to die this year in the shelter’s euthanasia room for the same reason: No one wanted her, and new arrivals needed the space.

The root problem, say animal activists, is overpopulation, and a non-binding question on the Nov. 6 ballot asks voters if they’d be willing to spend a few dollars a year to stop it.