I know that my teacher uses a lot of songs from musicals when she's in the mood for it (she choreographs musicals for a local student theater) so I was searching my mind's vast catalog of show tunes (I, admittedly, also work at a musical theater. I can tell you two things about it: 1- through-composed musicals are proof of an evil entity at work in the world, and 2- there are a LOT of sex jokes in old musicals.) and coming up trumps.
Tonight, finally, she mentioned the name of the song: "The Man I Love" by Gershwin. AH HA! I knew it was something I recognized! Not from musicals, though. No, I recognize it from my collection of Billie Holiday tunes (I freakin' LOVE Lady Day) that played near-constantly during a certain period in my life. I have always been rather fond of the sincere simplicity of the lyrics in songs of the era. Simplicity you couldn't (or shouldn't, more like) get away with now for fear of sounding trite and precious, cliché and condescending. Can you tell I don't listen to a lot of popular music these days?
Now that I know what song it is I can totally sing you the entire thing by heart. Here is the version I am familiar with. The barre version is an up-tempo piano number, naturally.