He began his professional career as a songwriter for Shalimar Music in 1957. He composed "Start Movin' (In My Direction)" for Sal Mineo and "Rockin' Shoes" for the Ames Brothers. In 1959, he recorded a cover version of Cliff Richard's "Living Doll" for Kapp Records, and it became a mild placed charter for him on the U.S. Billboard charts. He wrote songs for Elvis Presley throughout the 1950s and 1960s, which include "I Got Stung", "Come Along", and "Sand Castles". "Your Hand, Your Heart, Your Love" became a 1960s hit when it was performed by Andy Williams. In 1962, Hess wrote and recorded "Speedy Gonzales", (as David Dante) which became a #6 single for Pat Boone in the U.S. and a #2 in the UK, selling more than 8 million copies worldwide. Hess then recorded two solo albums for Kapp Records, again topping the charts, this time with a top 10 folk hit titled "Two Brothers."