Returning from Woods Hole, Muller continued his Drosophila work at Columbia, but there was no permanent position for him and he went back to Texas when the University of Texas at Austin offered him a professorship in 1920.
It was here the foci that would characterize his career took shape - namely, mutation, the nature of the gene, and the use of genetics to help humanity. It was also here Muller performed the research for which he would be awarded the Nobel prize.
Muller and Altenburg spent the summer of 1922 in Europe, touring and (particularly for Muller) developing contacts with laboratories and universities. Especially notable were several weeks Muller spent in the newly formed Soviet Union. Not many scientists had been Bolsheviks before the revolution, but the new government took a light hand with them. The priority, for the moment, was modernizing the economy rather than enforcing ideological purity. Muller found the scientists optimistic and exuberant about their research, and gifted some Drosophila strains to the Soviet geneticist Alexander Serebrovsky. Muller's visit led to enduring connections with Russion geneticists and greatly aided the development of fly genetics in the USSR.
Back in the States he married Dr. Jessie Marie Jacobs, a mathematician he originally met when he asked her for help with data analysis. Their child, David, was born in 1924. Illustrating the Texas political sentiments that had long bothered Muller, the mathematics department fired Dr. Jacobs Muller when she became pregnant, on the grounds that she could not adequately attend to both motherhood and a career. Brilliant and motivated, this haunted her for years to come and was a factor in the demise of their marriage.