Allison won the Wimbledon doubles title in 1929 and 1930 with partner John Van Ryn. They are considered by many tennis historians to be the best doubles combination of the period. Perhaps Allison's finest moment as a singles player came on June 30, 1930, when he upset the legendary Henri Cochet of France in the quarterfinal round of the 1930 Wimbledon tournament. However, he lost the championship in the finals to fellow American Bill Tilden in straight sets.
Allison achieved the number-one ranking in the United States in 1934 and again in 1935 and won the United States National Open Championship in 1935 by defeating Fred Perry in the semifinals and then Sydney Wood for the title at Forest Hills, New York. Along with partner Van Ryn he claimed National Doubles in 1931 and 1935 and finished second in 1930, 1932, 1934, and 1936. Allison competed on behalf of the United States in Davis Cup competition from 1928 until 1937. He retired from full-time competition in 1937 after a serious injury to his lower abdomen. Upon retirement, he served as an assistant to Penick at the University of Texas from 1938 to 1941, when he left to join the army air corps; he achieved the rank of colonel. After his discharge he returned to the university in 1947 and served as Penick's assistant until 1957. That year he became the head tennis coach at the university, where he served until his retirement in 1972. He instituted a policy restricting athletic scholarships for tennis to players from Texas. His teams won four Southwest Conference team championships, three singles titles, and one doubles title. He was elected to the Texas Sports Hall of Fame in 1957 and is a member of the Longhorn Hall of Honor. In 1963 he was enshrined in both the national and international tennis halls of fame.
Allison died on April 20, 1977, of a heart attack, only four days after the dedication of the new University of Texas tennis facility in his and Penick's honor. He is buried at Oakwood Cemetery in Austin. He was survived by his wife, Ann (Caswell). The couple had no children.
30° 16.565, -097° 43.517