The Plimsoul's big break came when their song "A Million Miles Away" was used in the movie Valley Girl. In fact, the band actually performs in a scene in the movie. Surprisingly, Valley Girl became a modest hit, and interest in the band soared. This coincided with the recording of their second album, 1983's Everywhere at Once, which should have been great, but ... the recording sessions went quite badly, and Case broke The Plimsouls up in order to go solo. Although Case has generated some amount of critical acclaim through the years, he never quite found his audience, leaving him (and The Plimsouls) as a one hit wonder.
Cool trivia fact: Peter Case's previous band, The Nerves, wrote and recorded the original version of "Hanging on the Telephone" in 1976, which was covered by Blondie (and became a hit for them in 1978).