Saxophonist Karl Denson visits New Orleans every year during Jazz Fest. The tradition began two decades ago with his acid-jazz-funk band, the Greyboy Allstars. This year the Greyboy Allstars and Denson’s hard-hitting jam-funk-rock band, Tiny Universe, are both playing evening shows after the Jazz Fest gates close.

Denson’s other claims to fame include playing sax with the Rolling Stones, a gig his four years in the stud...