Mats Gustaffson, Ingebrigt Håker Flaten and Paal Nilssen-Love make up one of the great backing bands music has produced. Like Booker T and the MG's, The Band and the Bar-Kays, the Dap-Kings Like a freeform Muscle Shoals Wrecking Crew, they have been at the ready to work with the likes of Thurston Moore, Jim O'Rourke and Otomo Yoshihide. They have an inspired way of remaining ever themselves (and they are three players with very recognizable voices) while wholly supporting their added members, from the beautiful bass voicings that came from their album with Barry Guy (Metal, No Businness, 2012) to the saxophone exhilaration of their work with Joe McPhee.

But on The Cherry Thing they have found their most inspired meeting yet. It's the band's first project with a singer, and Neneh Cherry is almost too perfect a choice — not only because she is a versatile singer who can swing and groove but because it was a composition by her father, the late trumpeter Don Cherry, that gave the band it's name.

The surprises are in no short order on The Cherry Thing and the group wisely avoids obvious paths. They don't revisit Cherry's hits from the '90s or rely on her father's world jazz or draw allusions to the Slits, the punk-reggae band she sang with as a teen. Instead they invent something new, navigated by their choice of material. There are a couple original compositions here, by Cherry and Gustaffson, but the album is dominated by wisely selected covers. They spend a luxurious 8½ minutes with Suicide's "Dream Baby Dream," find a subtle sweetness in MF Doom's "Accordion" and make a remarkable bari-driven thrust of the Stooge's "Dirt." And while the project isn't defined in terms of the man who gave both the band and the singer their names, they do a nice version of his "Golden Heart" with quiet African percussion and gently processed vocals and get to their jazziest with a take on "What Reason Could I Give?" (here simply called "What Reason"), an unissued cut from Science Fiction, one of the many albums Ornette Coleman made with Don Cherry.

It's an unusual setting for a singer. With no chordal instruments, Cherry is a bit out on her own (although Gustaffson and Flaten both make use of electronics, filling some of the sound field). She's a strong enough singer to go it with just the root of accompaniment — and perhaps this was being referenced in the selection of "Too Tough to Die," a song by Martina Topley-Bird whose voice was often left floating on all alone on Tricky's. It's a very different vibe than those post Massive Attack illbient tracks, but that's a gap that might be closing. In November they're releasing an album of remixes by Lindstrøm & Prins Thomas (who've reworked the Boredoms and Franz Ferdinand) along with Jim O'Rourke, Lasse Marhaug. Merzbow and others. The Cherry Thing can make anything its own.