The comedian, who turns 68 this year, told Letterman that everything was "going great" with the baby, and that his wife was a great mother.
He then placed a baby monitor on Letterman's desk.
"The baby's back at the hotel," Martin explained. "and I'm a responsible dad."
What followed were noises from the monitor, including a dog barking and a siren -- "I think I left the window open!" Martin said.
Letterman asked about the baby's name.
"We've thought about the name quite a bit," Martin said. "Conquistador."
"What do you think? I didn't want to go with one of those Hollywood... weird names."
"Conquistador says... It's a statement."
Martin will make us wait for further details -- for now, we can assume he's as protective as he was as George Banks in "Father of the Bride."
Putin thinks Obama would save him if he were drowning
Rosie O'Donnell unveils nearly 50-pound weight loss