By 1928, however, Miez was the world's leading gymnast. He overcame a poor performance on the parallel bars to win the individual all-around title, and he also earned gold medals on the horizontal bar and in the team event, as Switzerland edged out Czechoslovakia in a close contest. Miez won a silver medal on the pommel horse, finishing just behind his Swiss teammate, Hermann Hänggi. He also placed fourth in the long horse vault and eighth on the rings.
Miez travelled to Los Angeles for the 1932 Olympic Games, but because he was the only Swiss gymnast to do so, he was limited in the events he could enter. He ended up competing only in the floor exercises, earning a silver medal. In 1936, Miez, already 31 years old, participated in his fourth edition of the Olympic Games, and he won a gold medal in the floor exercises, a silver in the team event and placed eighth in the side horse vault. This brought his career medal total to eight: four gold, three silver ones and one bronze. Miez devoted the rest of his long life to the promotion of gymnastics as a sport.