"I have too much respect for Dave to do anything that would distract viewers from watching his final show," Kimmel told The New York Times in an email. "Plus, I'll probably be crying all day, which makes it hard to work."
The Times reports that NBC's The Tonight Show -- which launched Letterman's career only to have Jay Leno host the show when Johnny Carson retired -- will air a new episode with Jimmy Fallon in the hosting seat.
Meanwhile, Conan O'Brien -- who took over Late Night when Letterman went to CBS' Late Show -- plans to pay tribute to the 68-year-old host on his TBS program but will still run a new show on May 20.
Comedy Central hosts Jon Stewart and Larry Wilmore didn't even have to decide whether to air a new episode during Letterman's last night. Both The Daily Show and The Nightly Show are already in repeats that week.