Speaking of REM, you might like The Corrs. I don't mean their studio albums though, as they're really a rather predictable pop band, but check out their acoustic Unplugged DVD. They do several beautiful performances of traditional Irish music (especially "No Frontiers") amongst their chart hits. They also do a cover of "Everybody Hurts", which I must say I prefer to REM. Cheeky, I know ...
Interesting thread once again, Touti. But why did you sell them, if you don't mind me asking?
Anouk is a versatile artist although she seems to be more inclined to fairly heavy rock. "Update" contains unplugged and much softer versions of her material except for one song that's still a bit heavy.If you plan on getting music from her I suggest you start with that album and go with the other stuff if you like it.