With record producer George Martin, Kramer's first hit was "Do You Want to Know a Secret", a Lennon-McCartney song from Please Please Me. It was a #2 British hit in 1963, and was followed by yet more Lennon-McCartney songs, including "Bad to Me", "I'll Keep You Satisfied", "From a Window" and "I'll Be on My Way". Kramer's biggest hit was the ballad "Little Children", his only major hit outzside of the UK. His back-up band, the Dakotas, had some success on their own with a mostly instrumental tracks. Kramer's last hit was "Trains and Boats and Planes" (from 1965, written by Burt Bacharach-Hal David).