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A strange thing happened a few years ago when Christine Longnecker, who teaches horseback riding in and around Erie County, Pa., brought her new rescue dog, Miles, to a class. Instead of waiting quietly with the other non-horses in the barn, Miles suddenly sprinted into the ring and bounded over the fences himself.

“He looked so excited,” Ms. Longnecker said. “And then he turned and barked as if to say, ‘This is how you do it.’”

That was the beginning of Miles’s career as an agility dog — the sort of dog you might see sprinting over and through obstacles while its owner frantically rushes around, yelling commands. On Saturday, he competed for the second time in the agility competition at the Westminster Kennel Club Dog Show, which was held in Flushing, Queens.

The agility competition might be the rhythmic gymnastics of Westminster, derided as less than by traditionalists, but it’s a growing sport with meritocratic principles and an air of antic fun in its favor. While Tuesday’s classic dog show finals, with best in show on the line, are open only to good-looking purebred dogs — never mind if they’re indolent, overbred or a couple of biscuits short of a box — the agility competition rewards speed, intelligence and enthusiasm. Any dog can compete, no matter who its parents are.

Miles is an All-American dog, the American Kennel Club’s name for mutts. He looks vaguely Doberman-y, with a partially black, shiny coat and a long snout, but he’s actually 40 percent cattle dog, 23 percent Labrador, 10 percent Border collie and 27 percent mélange of hound, according to an Embark dog DNA test commissioned by Ms. Longnecker.

He is also an unlikely success story: a once virtually unadoptable rescue dog who now competes against the top agility dogs in the country.