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."