He caught a break in 1985 when he was asked to join the Broadway show "Sugar Babies" with Mickey Rooney and Ann Miller, replacing an outgoing variety act. For the naive and devoutly-raised Dunham, Broadway was a new world filled with beautiful showgirls and crusty stagehands, and his first taste of entertainment industry egos came when Rooney called Dunham into his dressing room, and told him he was there for one reason alone: so that Rooney could change his costumes. He performed at the Westbury Music Fair on Long Island. These early experiences, in which he used characters like José Jalapeño on a Stick, taught him the value of modifying his act regionally, as the jalapeño jokes that worked well in Texas were not as well received by audiences in Long Island. After graduating from Baylor University in 1986, he continued honing his act in comedy clubs in the Southwest with new characters such as Peanut and José Jalapeño, but struggled against the perception he relates from fellow comedians that he was not a true comedian because he relied on props.