Soulsavers are no band, but rather a "production team" (at least, this is what the internet says) - as long as this "production team" uses the gifts of musicians like Mark Lanegan, they might be called whatever one likes them to call (with the exception of derogatory terms).
Here are two songs in their interpretation: 1st one (from "Broken") "You Will Miss Me When I Burn", written by Will Oldham (aka Bonnie 'Prince' Billy), vocals by Mark Lanegan.
A second one, "Some Misunderstanding" (also from "Broken"), written by the great Gene Clark of Byrds fame, vocals by Mark again.
The bonus song is a cover of the Jagger/Richards piece "No Expectations", originally featured on the "Beggar's Banquet"-album and as the b-side of the "Street Fighting Man"-single. It is the last track on the Soulsavers album "It's Not How Far You Fall, It's the Way You Land", vocals by Mark Lanegan again.