David Letterman publicly apologized to his wife Regina Lasko during the taping of tonight’s Late Show. He also apologizes to his staff for all the scrutiny the show has received since he admitted to having sex with staff members. “I’m terribly sorry that I put the staff in that position. Inadvertently, I just wasn’t thinking ahead,” says Letterman, according to the show’s transcript released by his spokesman this afternoon. “And moreover, the staff here has been wonderfully supportive to me, not just through this furor, but through all the years that we’ve been on television and especially all the years here at CBS. So again, my thanks to the staff for, once again, putting up with something stupid I’ve gotten myself involved in.”

As for his wife, Regina, Letterman says, “she has been horribly hurt by my behavior, and when something happens like that, if you hurt a person and it’s your responsibility, you try to fix it. And at that point, there’s only two things that can happen: either you’re going to make some progress and get it fixed, or you’re going to fall short and perhaps not get it fixed, so let me tell you folks, I got my work cut out for me.”

The show’s guests Steve Martin and Martin Short also apparently joked with Letterman about the news. CBS released the following clip of tonight’s monologue: