 Houston joined the Southwest Conference in 1976, and the Cougars posted a 10–2 record that included a 30–0 win at rival Texas and a victory over Maryland in the 1977 Cotton Bowl Classic.Yeoman finished as the runner-up for the AFCA Coach of the Year award and won Coach of the Year in the state of Texas.During Yeoman's career, the Cougars won four Southwest Conference Championships (1976, 1978, 1979, 1984), and he earned a 6–4–1 record in bowl games including a win over Nebraska in 1980 Cotton Bowl Classic.