In what NBC News is billing as David Letterman’s first in-depth TV interview since leaving his CBS show, David Letterman said he does not know why CBS did not give his Late Show to a woman. “That would have been fine,” he told former NBC Nightly News anchor Tom Brokaw for Sunday’s Dateline NBC.

On the other hand, nobody asked him, Letterman said. When asked “Did they ask you about who should replace you?” Letterman laughed, “Oh, no. No, they didn’t ask me about anything. They were just happy I was going.”

Letterman said he thought he would miss late-night TV, until he watched the first night of Late Show with Stephen Colbert hosting. “When he went on the air — an energy left me and I felt like, ‘You know, that’s not my problem anymore.’ And I’ve kind of felt that way ever since.”

“I devoted so much time, to the damage of other aspects of my life,” Letterman said of his late-night career. “It’s good now to not have that. I couldn’t care less about late night television.”

NBC, from which Letterman dramatically decamped in 1993 after losing an internecine battle for the Tonight Show job,  is airing Letterman’s interview to battle CBS newmagazine 60 Minutes at 7 PM this coming Sunday. NBC, the network Letterman routinely described as being run by “pinheads” during his time at CBS, is using this exclusive ratings-magnet interview as part of its On Assignment limited series.

While NBC’s airing David Letterman talking about CBS, CBS’s 60 Minutes will be rebroadcasting its Hamilton segment, with previously unseen material about the Broadway sensation that’s up for a record 16 Tony Awards – which CBS is airing right after the newsmag that night. CBS News advises that fans of Hamilton who have not had a chance to see the Broadway production may want to watch because it could be their last chance to see Lin-Manuel Miranda, the show’s creator, acting in the title role. Miranda will move on later this summer.  The segment rebroadcast is nearly double the length of Charlie Rose’s original report, first broadcast last November.