Carissa Harrison had grown concerned. First, she realized the hair around her English bulldog's mouth had turned an ominous gray. Then she noticed the lazy way in which he had begun to rouse himself in the morning. Normally active, Mac had also turned into a bit of a couch potato during the day: He showed less interest in playing, and he panted volubly while hefting himself off the floor. Harrison's beloved meatball of a puppy had become elderly. How much more time, she began to wonder, could he have left?

With this in mind, Harrison found herself one sunny morning in Seattle seated in the waiting room of VCA Veterinary Specialty Center of Seattle, a veterinary emergency room and hospital. On one side of the room, a man in a rumpled black T-shirt, shorts, and tube socks sits murmuring quietly to himself. On the other, a woman in a floral muumuu whispers into the ear of a Chihuahua-Pomeranian mix: "Poor baby. Do you need to go potty?" But the man sitting directly next to her is cheerful. He shows her a cellphone picture of a German shepherd and a keeshond in dog-size football jerseys and little hats.