Keely Smith’s astounding voice and exotic beauty were a prime ingredient in Louis Prima’s show business success. At 68, she’s enthralling a new generation of music fans with her Swing Swing Swing album, a disc that proves you don’t have to wear a zoot suit to "Jump, Jive an’ Wail!"

In 1948, 16-year-old vocalist Keely Smith joined the band of native New Orleanian Louis Prima. On July 13, 1953, Smith and Prima were united in marriage...