Typically, when Greenville, Mississippi and music are mentioned in the same breath, Delta blues singers come to mind—like Lil' Dave Thompson, Willie Foster, Roosevelt "Booba Barnes, and Eden Brent.

For years Tyrone Davis has recorded little but standard soul-blues ballads and cloying, swaggering hoochie-man numbers (“Sugar Daddy,” “Tip Toe Through the Bedroom”). But last year’s Come to Daddy ...