In the 1920's Spielmann was to have his greatest successes. He won Semmering 1926 ahead of Alekhine and Nimzowitsch. Another top result came in Karlsbad 1929, where 12 of the world's 13 top players participated (Chessmetrics). The 46-year-old Spielmann started with 9/10 before tiring in the second half, even if he won against Capablanca (his career score against the Cuban was an impressive +2 -2 =8). During the last round it still looked as if Spielmann might win the tournament, but eventually he ended up 0.5 behind Nimzowitsch.
Spielmann was still playing in the 1930s, when the title challengers faced him in matches before playing World Champion Alekhine. In these matches Spielmann defeated both Bogoljubow (1932) and Euwe (1935). In Moscow 1935 he finished 5th of 20 players, one point behind fourth placed Capablanca. His last good result was Margate 1938 (second behind Alekhine).
A good biographical article in German is Rudolf Spielmann: Lebensgeschichte als Zeitgeschichte.