Wow, I remember that from over twenty years ago but I haven't seen it since.
This was when Sting was shopping Brimstone & Treacle.

The part that stands out in my mind was when Sting had an itch on his back and Dave scratched it for him and then said:

"That was more fun than I thought it was gonna be"

In a message dated 7/3/03 2:26:48 PM Eastern Daylight Time, F.Berthelot@Ramsa.com writes:

The TRIO channel is airing an old David Letterman show tonight from 1982 featuring Sting as guest.