I am quite in love with this song today, but have no idea what the name of it is. I must investigate.(exciting results below!)
So, I have investigated and come up with some answers. The song is called "Martha Ann", and the reason I had trouble finding it is because it will be released on David's forthcoming fifth album. Yay! His last album, Sharp Teeth, is a real treat, but has one of the most disturbing album covers ever. Take a look here if you are prepared to be freaked out.