Tozer performed at the inaugural concert of the Melbourne Concert Hall in 1982. In the early 1980s he taught at the University of Michigan. From 1983 he based himself in Canberra and briefly taught at the ANU School of Music, Australian National University before his touring and recording schedules made this impractical. His early recordings were not commercially released; his first commercial recording, in 1986, was of John Ireland's "Piano Concerto in E-flat major" with the Melbourne Symphony Orchestra conducted by David Measham, still considered by many the best recording of the work. In 1989 he worked with Peter Sculthorpe to record a disc of Sculthorpe's works for piano and strings.