The Flatlanders, "Dallas"
Odd but true: Jimmie Dale Gilmore has a small part in The Big Lebowski. This is sort of like finding out that Sonic Youth's original drummer was in Ferris Bueller's Day Off.
I first heard this song when it was covered by R.E.M., at some shows they did in London with Billy Bragg, Robyn Hitchcock and a few others, which appeared on a "rare concert recording" someone was nice enough to make a copy of for me back in the halcyon days of the internet. I knew it was a song by a band called The Flatlanders, but could find no other information about the band, much less any of their recordings; I chalked it up to a name that had been misheard or mis-transcribed. Turns out that the album was out of print, hard to find, or perhaps nonexistent when I was looking for it.
The brilliance of the song is that it works as a slow song or a fast song, and it uses its chord changes to good effect--each one intensifies the song by going down, rather than up.