Most western singers use only the Simon tune.

Katie Lee wrote, "The melody I've always heard and sung is far too sophisticated to be the work of someone like Billy Simon. I'm even more convinced of this now that I've seen and talked with him, but am prepared to keep my mouth shut about it unless he offers some explanation of where he got the tune.
"From somewhere his guitar appears.
""Lord, I can't play that thing no more. I got arthritis in m' hands so bad my fingers won't stick on the strings."
"Try, I say. "Otherwise how am I going to hear the right version."
[Simon-] "Right? I dunno it's right. It's the way I sing it."
[Simon sings....]
Katie Lee continues, "A simple, three-chord melody, no fancy minors, no bridge after the first four lines (where all the other versions change melodic line), only the same melody repeated again, all through the song. Any cowboy could sing it, hum it, play it and pass it on in one night's learning. It is Billy's tune all right- before the non-cowboys got wind of it."

And a damn sight better than with that addition by Niles.

Katie Lee, 1976, Ten Thousand Goddam Cattle, Northland Press, Flagstaff.