In December 1964, Cunningham and the Mighty Avons had a Top-10 hit with the song "Tribute to Jim Reeves", which also entered the British charts (the first time for an Irish artiste), and played on Top of the Pops (also an Irish first), which further boosted their career. Their major hit was "Lovely Leitrim" in September 1965, which stayed at number one in the charts for four weeks. As well as regularly touring Ireland to large crowds, the Avons made many appearances on television, and often played in Britain, the USA, and other places.