This may be completely wrong, but I wonder if that's the tune which Diana
> sang on the soundtrack of the Clint Eastwood film "True Crime"
> (1999). If so, I believe the tune was also written by Eastwood, wearing
> another of his many hats.

Nope - the song Diana sang for "True Crime" was "Why Should I Care?" "I'll Make It Up..." is from "The Score"

It was issued as a one-track cd for Oscar voters, for their consideration for an Academy Award. Other than that, there hasn't been an official release of the track.