In 1929 Gledhill won the national junior singles and, partnering Ellsworth Vines, doubles title.

In 1932, Gledhill and partner Joe Coughlin won the NCAA Doubles Championship.

In the quarter finals, Gledhill was 2 sets to 0 and 5–3 down against the finalist of the previous three years, Harry Hopman, but fought back to win.

[5] Gledhill then beat Vivian McGrath before losing in the final to Jack Crawford.

Gledhill turned professional in early 1934 and joined a tour with Bill Tilden and Vines.