Joe Cocker’s career, which took off with a bang at the Woodstock festival, has in recent years threatened to die with a whimper. His latter-day concerts have resulted in tales of onstage drunkenness while his last album, 1976’s Stingray, attracted little but bad press. It began to seem that he might be best remembered as the subject of an uncanny impersonation by Saturday Night Live‘s John Belushi.

Before you take any bets on that, however, listen to Luxury You Can Afford, an Allen Toussaint–produced label debut, which suggests the possibility of a comeback. One plus is the varied, well-chosen program, which intersperses evergreens like “I Heard It Through the Grapevine” and “A Whiter Shade of Pale” with new tunes written especially for Cocker. Also helpful is the stellar backup crew, which features Dr. John, Rick Danko, Toussaint, and others. But the biggest asset here is Cocker himself: he’s interpreting imaginatively again, and he seems to have recovered a lot of the spirit that imbued his early releases.