In the 1933/34 edition, also won by Riumin, Kan placed 5th. In 1934, he took 5th in Leningrad (Botvinnik won). He tied for 6-7th at Moscow 1935 (2nd it; Botvinnik and Salo Flohr won). In 1936, he tied for 7-10th in Moscow (3rd it; José Raúl Capablanca won). In 1936, he tied for 1st-2nd with Vladimir Alatortsev in Moscow–ch. In 1937, he took 4th in Moscow–ch (Alatortsev and Sergey Belavenets won). In 1937, he took 2nd, behind Reuben Fine, in Moscow. The website Chessmetrics.com, which retroactively rates older players, ranks Kan as 13th in the world in 1944.