As was common in their day, The Kangaroos began to move around between territories to avoid overexposure. The team arrived in Championship Wrestling from Florida billed as NWA Florida United States Tag Team Champions. It was a tag team title they never technically won, but were instead awarded by the promoter. The Kangaroos stayed in Florida, defending against all challengers until the duo of Eddie Graham and Dick Steinborn took the United States titles from them in a match on 1 November 1961. In 1962, The Kangaroos once again traveled across the United States, working for the Midwest Wrestling Association of Ohio where they held the Ohio version of the NWA United States tag team title. They also toured Japan with the Japan Wrestling Association and were the first to hold the Japanese version of the NWA International Tag Team Championship. In 1964, Costello and Heffernan made their west coast debut, working in Los Angeles, California for the World Wrestling Association (WWA) where they beat Édouard Carpentier and Ernie Ladd for the WWA World Tag Team Championship. The Kangaroos held the titles for three months before losing them to the Torres brothers (Alberto and Ramon) on 28 April 1964.