If you've ever heard a great song recorded in New Orleans sometime in the second half of the 20th century, chances are pretty good Allen Toussaint had something to do with it. He's a songwriter, producer, arranger, pianist and (occasionally) singer, who's worked with with Elvis Costello, Paul Simon, the Meters and many others. The Bright Mississippi is something else again — Toussaint's first foray into (nearly) all-instrumental jazz. It's an homage to New Orleans in pop, gospel, jazz and blues, written in, about or associated with the city. As overproduced as much mainstream music is these days, Mississippi is gloriously under-produced — you practically feel like you're eavesdropping on a private session. Toussaint's piano — elegant and blues-rich — is front and center; he certainly doesn't skimp on the notes, sounding opulent rather than cluttered. Accompaniment is both sparing and superb: Nicholas Payton's crackling, emotive trumpet, Marc Ribot's delicate yet pointed guitar, Don Byron's soulful clarinet, and on one track, the gorgeous, slightly rough, big-toned tenor sax of Joshua Redman. — Mark Keresman