Just You, Just Me
The tune is from 1929, and its characteristic is that the melody of the chorus starts halfway into the first bar. There are many nice recordings, a dance band recording with Smith Ballew around 1930, and several jazz versions by tenor sax players like Coleman Hawkins, Don Byas, and Lester Young, just to mention a few. It also got a boost from Woody Allen when it was featured in his film Everyone Says I Love You.