For a fighting chance against disease, people will sometimes go to unlikely places -- even, it turns out, to the boxing ring. Our Cover Story is reported by Lesley Stahl of "60 Minutes":

Aaron Latham sparred with his boxing coach, Roberta Marongiu. "Gimme all you got, come on!" she said.

He -- and everyone else in the class -- has Parkinson's.

It's a progressive neurological disorder that affects nearly a million Americans. You don't hear about very many with the disease getting better.

"I think of Parkinson's as being the incredible shrinking disease," said Latham (who is also Stahl's husband). "It doesn't shrink itself. Parkinson's doesn't shrink. Parkinson's shrinks you."

Latham and his fellow Parkinsonians, aged 45 to 92, are part of a new program that aims to stop the shrinking, If not reverse it.

Aaron Latham, who has Parkinson's disease, works out at Gleason's Gym in Brooklyn. CBS News

Each exercise works on a symptom.

"Gimme ten. Up!"

Stretching is for their stiffness; footwork for balance; punching to steady their tremors ...

"Boom. Yaaaaaaaa!"

Shouting to counter their soft-voice syndrome; and sparring for coordination.

Stahl asked, "What does boxing do for you, then?"

"Boxing's just the opposite of Parkinson's," Latham said. "Instead of to shrink you, everything's designed to pump you up. First of all, you get to put on these great gloves. It gives you enormous, giant hands and a different attitude toward the world. You get your physical courage back and your mental courage seems to kinda come along."

The program, called Rock Steady Boxing, uses professional boxing techniques (maybe a little more gently). Developed in Indianapolis in 2006, it has spread to over 50 gyms worldwide.

When Italian-born Roberta Marongiu first saw Rock Steady at a medical conference, "I just thought it was genius. 'Why didn't I come up with this?'" she laughed. "I thought it was an amazing program."

When she's not coaching, Marongiu is a researcher at the Weill-Cornell Medical College in New York, working on gene therapies for Parkinson's.

"My main goal has always been the quest for a cure, finding a cure," she said. "But lately in the last couple of years, I felt there was something missing. And when I found this program, I thought it was something that I could do to help right now, in the present."

Roberta Marongiu, of Rock Steady Boxing. CBS News

So two years ago she and her husband, Alex Montaldo, an actor, went to Indiana to learn how to teach Rock Steady.

They then approached the folks at Gleason's in Brooklyn, a kind of grungy, no-frills, old-school gym, where Muhammad Ali trained, and where Robert De Niro trained for "Raging Bull."