03/03/2012 at 02:00 PM EST
His taste for ties and perfectly pressed suits earn Don Draper serious style points week after week on Mad Men
But Jon Hamm
, who plays the advertising titan on the AMC period drama, can recall one accessory that didn't exactly stand out for the right reasons in his wardrobe on the show: a removable cast.
Hamm, 40, had to wear the cast when he broke his hand on-set the first season, just one of the three injuries he told David Letterman about on Thursday's Late Show with David Letterman
"I have this sort of bear-claw swollen hand," said Hamm of the damage, sustained while rehearsing a war flashback scene.
"It looks like it's been over-inflated," he added, encouraging fans of the show – back March 25 – to consult their series DVDs.
Hamm, who was promoting his new film, Friends with Kids
, said he also separated his shoulder while performing stunt work and received eight stitches in his head after a piece of the set landed on him.
With blood dripping down his neck, he recalled, he sprung right into action.
"I immediately took my jacket off," he joked. "It was rented."