Sad/Morbid and or New Orleans-like Songs From the 30's? If You Know Any, Please Help Me Out - Comments

The first one that comes to mind is Billie Holiday - Strange Fruit, from 1939. It's actually a song about racism and lynching. The lyrics were originally a poem, and there have been plenty of covers of it, but I think Billie Holiday was the first to sing it.

I can only think of The House of Rising Sun by the Animals. But that's from the 60s...