Although it didn't originally have anything to do with their sound, the Cowboy Junkies' name wound up seeming pretty accurate: their music was grounded in traditional country, blues, and folk, yet drifted along in a sleepy, narcotic haze that clearly bore the stamp of the Velvet Underground. The vast majority of their songs were spare and quiet, taken at lethargic tempos and filled with languid guitars and detached, ethereal vocals courtesy of Margo Timmins. Over the late '80s and '90s, the group recorded a succession of critically acclaimed albums that found favor in the alternative rock community. Read more at allmusic.com
Download 12 (!!!) entire live shows from the Internet Music Archive in the .shn format
If you're unfamiliar with shn files, read this old article of mine.