Leigh became the primary punt returner for the famous 1972 Miami Dolphins team that had a perfect season and won Super Bowl VII. Leigh returned 22 punts for 210 yards and a 9.5-yard average for the 1972 Dolphins. The 22 punts returned ranked 5th in the NFL that season, and the 210 yards and 9.5 average each ranked 6th in the NFL that season. Leigh also returned six kickoff 153 yards, a 25.5-yard average, and rushed 21 times for 79 yards, a 3.8-yard average. Leigh got to play in Miami's 14–7 Super Bowl victory over the Washington Redskins, but did not have any carries or returns.
