Vangelis, "One More Kiss, Dear".
One of the more interesting Google search results I got had the following opening post, which expressed my thoughts well:
From here. I searched for a few of the names mentioned on that page and one of a few songs I found on the YouTube that sounded similar enough was Peggy Lee's "I Only Have Eyes For You".I'm looking for more music like the song "One More Kiss, Dear" from the Blade Runner soundtrack.
I'm looking for really old sounding stuff. Like a thin voice or recording, not one that's very full like Frank Sinatra, Perry Como, or even Bing Crosby (which I think was from the same time period that I may want music from). Helen Forrest is a female singer in the style I'm looking for. Nice, relaxing music that just sounds nice.
Before Googling for similar songs, Billie Holiday was obvious for me. Besides that, a few Christmas songs came to mind, most readily Nat King Cole's "The Christmas Song".