Short, who has been a guest on the evening talk show more than 50 times, saluted his friend in song.
Watch the interview and performance below.
The longest-tenured late-night talk-show host at more than 32 years, Letterman, who has hosted "Late Show" for 22 years, announced his retirement on the April 3, 2014, broadcast. Since its CBS premiere on Aug. 30, 1993, Letterman’s "Late Show" has won nine Emmy Awards and 73 Emmy nominations.
Letterman debuted on the late-night scene Feb. 1, 1982, with the premiere of “Late Night with David Letterman,” which ran for 11 ½ years and was honored with five Emmy Awards. As of May 20, 2015, Letterman will have hosted 6,028 total episodes of both “Late Night” and the "Late Show."
The "Late Show with David Letterman" is a production of Worldwide Pants Incorporated. Barbara Gaines, Matt Roberts, Jude Brennan, Maria Pope and Rob Burnett are the executive producers. Jerry Foley is the director.