Jones' most successful season was the winter of 1975/76 . He was able to classify himself in the top five three times, winning the giant slalom in Copper Mountain on March 5, 1976 . At the 1976 Winter Olympics in Innsbruck , Jones was ninth in giant slalom, eleventh in downhill and 19th in slalom . Taken together, this resulted in third place in the combined ranking. However, since this was not part of the official Olympic program, he received a bronze world championship medal. In the same season he also won the US downhill title.
In the winter of 1976/77 , Jones could no longer maintain this high level. His only top 10 classification was 9th place in the Hahnenkamm combination in Kitzbühel . At the end of the season he resigned from top-class sport.