I'm willing to bet this is on Letterman in 1990. Thanks Krysia for the alert!
EDIT: fan Phil has a VHS of this labeled 1989-- wowza, remember tapes? ;) Thanks Phil.
And as a postscript to the "Astrud" clip, Peter White chimes in the forum there:
"That certainly is Richard Elliot on baritone sax- he was brought in just for the Carson show and I think that I may have even recommended him. By the way, did anyone notice Marc Antoine on guitar? He did that tour with Basia(1987 or 1988?) as I was on tour with Al Stewart at that time."
That's pretty sweet, I had no idea that was Richard Elliot!