David Letterman has long been a champion of deeply strange American voices, as you know if you’ve ever seen footage of him interviewing Captain Beefheart. Tom Waits first appeared on Letterman’s NBC show in 1983, and he’s been on a number of times over the years. With a week left before his retirement, Letterman had Waits on one of his final shows last night. Waits used the occasion to debut a new song, something he hasn’t done in a while. It’s called “Take One Last Look,” and it’s a scraggly lullaby about leaving your home forever — a poignant thing for him to be singing about in this circumstance. Waits also sat down for an interview with Letterman, in which he tried out a series of daffy stand-up routines. George Clooney had handcuffed himself to Letterman in a bit earlier in the night, and Waits reduced him to chuckle-fits exactly twice. Watch the performance and the interview, as well as Waits’ original Letterman appearance, below.

Do you think Jay Leno will show up on that final Letterman show? He has to, right?