[3] In June 1929 he served as deputy judge of local court in Stuttgart and Tübingen, prior to an intermittent leave of absence from civil service, which allowed him, from 1930 to 1933, to work as a tax consultant to the administration of the diocese of Rottenburg.

Shortly before the start of World War II Müller was drafted and took part in the campaign in France as a camp office clerk.

[3] After the war, Müller became the leader of the CDU in the provisional state of Württemberg-Hohenzollern in 1947, and soon won a seat to the assembly, situated in Bebenhausen Abbey.

[3] Upon the joining of Baden and Württemberg into the significantly larger state of Baden-Württemberg in 1952, Müller's CDU became the predominant party and he replaced liberal Reinhold Maier as the Minister President.

Müller retained this post until he returned to his legal career as he was appointed to head the Federal Constitutional Court, now placed relatively close in Karlsruhe.