Gore recorded composer Marvin Hamlisch's first hit composition, "Sunshine, Lollipops and Rainbows", on May 21, 1963, while "It's My Party" was climbing the charts. Her record producer from 1963 to 1965 was Quincy Jones. Jones's dentist was Marvin Hamlisch's uncle, and Hamlisch asked his uncle to convey several songs to Jones. "Sunshine, Lollipops and Rainbows" was released on the LP "Lesley Gore Sings of Mixed-Up Hearts", but did not surface as a single until June 1965. Hamlisch composed three other Gore associated songs: "California Nights", "That's the Way the Ball Bounces" and "One by One". "That's the Way the Ball Bounces" was recorded September 21, 1963, at A&R Studios in New York; it was released as the B-side of "That's the Way Boys Are" and appeared on the LP "Boys Boys Boys". "One by One" was an unreleased track recorded on July 31, 1969, in New York and produced by Paul Leka; it first appeared on the Bear Family five-CD anthology of Gore's Mercury work entitled "It's My Party" (1994).