Here's a partial rare demo of a song written by Elton John and Bernie Taupin especially for Frank Sinatra. Sinatra was performing the song live in 1978, but never officially recorded or released it. This is part of Elton's demo of the song.
You can hear Frank Sinatra sing it here:
http://youtu.be/WpPBE8RAmnM?list=UUrI5FA66QgK7EycsKG6Qddg