Allen Toussaint’s music, which has been performed by everyone from Irma Thomas to Little Feat, is all about feeling. When done right, Toussaint’s songs take on a funky depth that’s rare in pop music. But in the hands of the wrong musicians, these songs can become generic, the type of music that wide-eyed tourists expect to hear on every New Orleans street corner.

Swingadelic is a 14-piece band of New York jazz musicians who clearly get a kick out of Toussaint’s music. On Toussaintville, they mostly succeed in their sleek interpretations, bringing a touch of Big Apple sophistication to the proceedings. At other times, the sleekness teeters on the edge of sleaze, as in the band’s limply swinging take on “What Do You Want the Girl to Do.” Trombonist Neal Pawley’s vocals on “On Your Way Down” are similarly soulless and suggest that the singer should have stuck with his main axe.

But these are only two minor missteps in an otherwise fine album. John Bauers, who sings most of these songs and even contributes the album’s only non-Toussaint composition, does a great job on classics like “Sneakin Sally Through the Alley” and “Working in a Coal Mine.” Other highlights include the instrumental takes of “Get Out of My Life, Woman” and “Everything I Do Gonna Be Funky,” where the musicians get to let loose and show off their considerable chops. All in all, this is a fun and funky album that puts its own spin on the Toussaint songbook.