He is credited with introducing rock and roll music to Iceland, performing there in May 1957. By 1958 the Rockets had become a jazz group with Scott and Tubby Hayes. During the following year, Crombie started Jazz Inc. with pianist Stan Tracey. In 1960, he composed the score for the film "The Tell-Tale Heart" and established a residency at a hotel in Monte Carlo. In May 1960, he toured the UK with Conway Twitty, Freddy Cannon, Johnny Preston, and Wee Willie Harris.