As well as Leaks did in 1972, he was even better in 1973 as a junior. He was again the team's leading rusher and set a school and Southwest Conference rushing records with 1,415 yards. He also set or tied 7 other school records that season, including the conference record for most yards in a game when he ran for 342 yards in a 42–14 win over SMU. This was only eight yards short of Eric Allen's NCAA record of 350 yards, set two years earlier in 1971. Leaks was again named All-SWC, as well as a consensus All-American. He finished third in the Heisman balloting, which made him only the fifth Longhorn Heisman finalist and tied him with James Saxton's 1961 performance for the best Longhorn Heisman finish. Texas went 8-3 in 1973 and won another Southwest Conference title and were ranked eighth, but lost the Cotton Bowl 19–3 to #12 Nebraska and finished fourteenth.
