“You can’t choose where the body loses fat,” he said.

Gary Diffee, a professor of kinesiology at the University of Wisconsin-Madison who examined some of her claims, said, “Like many things of this type, the science seems to be a mixture of true, kind of true, true but irrelevant to the point she is trying to make, and wrong.”

“The main thing is that she is getting people to move,” Dr. Diffee said.

Indeed, the testimonials of clients who say that her workouts have transformed their bodies have earned her sobriquets such as “organic plastic surgeon,” perhaps her favorite. As for Ms. Paltrow, who has appeared in several of her DVDs, Ms. Anderson said: “She hid her problem areas so well before me that I’m like, ‘I really wish your naked butt was everywhere before me and after me.’ ”

The engaging Ms. Anderson has succeeded where many have failed, inspiring thousands of disciples to do her hourlong DVD six days a week. Her fans chronicle their efforts on message boards and blogs with titles like Teeny Tiny Quest, a nod to the body type Ms. Anderson is famous for helping to form.

Ms. Anderson said she found the 11,690 buttock-toning moves she had to perform over three days of filming one DVD more taxing than enduring any jabs at her methods. The moves, she said, had her collapsed “in the fetal position, wanting to die.” But she accepts criticism as “part of trying to create progress; you get called crazy, like any inventor.”

Her current plan is to create a new workout every 10 days for nearly every age, body type and price. It requires her to come up with so many new moves that her assistants film every class she teaches with an old Sony Bloggie camera, the footage stored and labeled for the next round of production.