 White was granted a medical hardship for the 2004 season.He was again a finalist for the Heisman Trophy in 2004, trying to become just the second player after Archie Griffin to win the honor twice, but instead finished third behind his Sooner backfield mate, runner-up Adrian Peterson, and winner Matt Leinart.White did win the Davey O'Brien Award for the second straight year, becoming the third quarterback ever to win the prestigious award two years in a row.