​Fighting back against Parkinson's - in the ring

Gleason's donates a ring for them three days a week.

"It's kind of curious -- I always heard that Muhammad Ali got Parkinson's from boxing," said Stahl.

"When you say boxing for Parkinson's, it's kind of counter-intuitive," said Marongiu. "But the difference is this: We do non-contact boxing, so they don't fight against each other. They can fight against Alex in the ring, and they love it! They don't get hurt, they don't get hit."

But what about Montaldo? He wears body armor in the ring. "Yeah, and I'm glad I have to. One of our boxers specifically, he's the very reason why I had to buy that."

"He hurt you?"

"It was good pain," Montaldo said, because the boxer had demonstrated how strong he'd become.

"I think I hit him a little bit too hard in his ribs," Les Mills said, "and he got home and he decided that it was time to get some body armor!"

"Was your right upper cut or something like that?" Stahl asked.

"Think it was the left."

Les Mills, who suffers from Parkinson's disease, spars with Alex Montaldo, of Rock Steady Boxing. CBS News

When Mills, a New York City teacher and gym coach, was diagnosed with Parkinson's, it hit him hard.

Latham recalled, "When he first came in, he was not in great shape, both physically and psychologically. He was pretty depressed. Didn't really wanna do much. Well, you should see him now!"

Mills continued: "When I first started coming in, I was not able to walk straight to the ring. I would have to wobble to the ring. It was very hard to walk. Now it's piece of -- I don't wanna say a piece of cake, I don't wanna sound cocky! But physically, it made a big difference."

Everyone Stahl spoke to in Latham's class said they've seen an improvement. Part of the secret is camaraderie ...

"Go go go!"

"Everything you got!"

Competition ... and getting "pumped up."

"Harder! Crush him!"

That's why the trainers act like drill sergeants.

"Knock him out!"

"The trainers don't let you relax," said Mills. "They make you do what you're supposed to do, not what you wanna do. They push you so hard that it becomes a habit, a good habit."