It's the simply beautiful "What'll I Do," written by Irving Berlin in 1923. Sinatra recorded it in 1947 and again in 1962 for the album All Alone, arranged by Gordon Jenkins. Here's the later version:
Sammy Cahn is credited with the famous observation on the changes in Sinatra's voice through the decades:
When he was young, in the '40s, he was a violin. In the '50s, he was a viola. By the '60s, he was a cello and when he got to the '80s, he was a bass. The music was still sweet. It was just played on a different instrument.Sinatra was approaching fifty here and his voice was maturing quite beautifully into that cello. I'm not the biggest fan of Gordon Jenkins's arrangements -- they're often too flowery for me -- but this one is almost spare where it counts most, behind the lines:
When I'm aloneVery nice.
With only dreams of you
That won't come true
What'll I do?
Bob Dylan includes "What'll I Do" on his new Sinatra tribute CD Shadows in the Night. I don't know whether he includes the verse Sinatra omitted, but if you'd like to hear it, Willie Nelson sings it here, Linda Ronstadt here.