It sounds like a punch line: a miniature llama.

It is actually an American novelty, and a work in progress. Just as teacup poodles were bred down from standard ones, small adult llamas have been paired off by breeders for the last 20 years or so, producing some that stay small — and others that do not.

“Fifty percent of what you receive do not wind up being miniatures,” said Pam Fink, who breeds mini llamas and is president of the American Miniature Llama Association. Since the miniature gene pool goes back only about six or seven generations, it is far less reliable than that of an older breed like toy poodles, she said.

To qualify as miniature, a llama must be no more than 38 inches at the front withers (or shoulder height) at age 3. That makes it about three-quarters the size of a standard llama, but still a little larger than a standard alpaca.

“I’m 5-foot-5, and my standard llamas come up and like to rest their head on top of my head, so I will scratch them,” Mrs. Fink said. “A miniature walks up — an adult — and looks me in the eye.”