Led several short-lived orchestras (his first was 'Sonny Lee & His New York Yankees' in 1931; he fronted another group, 1936-37), before commercial success with a big band organised in 1940, which included among its personnel the trumpeter
Pete Candoli, tenor saxophonist Corky Corcoran and Danish-born trombonist
Kai Winding. Dunham's theme song was "Memories of You", a track he had made his own as a soloist with the Casa Loma Orchestra in 1937.