While women have long danced in heels, Ms. Barrett’s classes are part of a trend in exercise regimens that focus as much, if not more, on the footwear as the footwork.

Of course, many experts—and common sense—warn that wearing high heels for extended periods can increase the risk of injury. In a recent study, researchers at Griffith University in Queensland, Australia, and the University of Jyväskylä, Finland, found that high-heel wearers experienced “alterations in muscle-tendon architecture,” which led to fatigue and strain. Chris Carty, one of the authors, said it is hard to assess whether working out in heels is more dangerous than simply walking in them, “beyond the risk of falling due to a reduced foot contact on the floor.”

The Crunch Fitness chain of gyms offers classes called “Stiletto Strength,” which require attendees to “bring your own heels.” The class aims to strengthen the legs, abdominals and back to support posture in heels. It also incorporates an aerobic portion where students “go into ‘work it girl’ mode,” the company says.