My River of Dreams Mandela Dilem'na'

Here is my Mandela Dilem'na' .. When David Letterman had his initial CBS show in 1993, I believe August, he had Billy Joel as the musical guest.
I recall Billy Joel playing NO MAN'S LAND as the song.. Then being interviewed. Could have been vice versa on that..

However what perplexes me is that I distinctly recall Joel ALSO playing River of Dreams--which was the popular song he released that same year. I believe this second song was playing during the closing credits of the program.

Old clips I find don't include that song. And no mention online exists that it was ever played..

I have a box of old video cassettes that one day I want to turn into DVDs if I ever have time in life to do it before the video rots.. I hope to find the initial Letterman show that I taped from TV that night.

This may be a long shot. But does anyone else remember this?