When Culp arrived in Houston, Bum Phillips was the defensive coordinator for Sid Gillman at the time. He had convinced the head coach to try a 3-4 defense, employing three down linemen and four linebackers, eschewing the standard 4-3 fronts of the day. In basically an exchange of defensive tackles who had threatened to jump to the World Football League, the Oilers acquired Culp and a first-round draft choice in 1975 from the Chiefs for John Matuszak on October 22, 1974. Both Culp and Matuszak had signed contracts with the Southern California Sun and Shreveport Steamer respectively. It eventually became one of the most lopsided trades in NFL history, which was made worse for the Chiefs when the Oilers selected Robert Brazile with the draft pick.