Nei won the Estonian Championship eight times (1951, 1952, 1956, 1960–1962, 1971, and 1974). In 1955, he tied for third through sixth place in Pärnu (Baltic Republics championships), an event won by Paul Keres.
Nei's success in Estonian championships is highlighted, including his multiple wins and a tie for third-to-sixth place in the Baltic Republics Championships in 1955.