In Grand Slam events, Gledhill and partner Ellsworth Vines won the doubles championship at the U.S. Championships in 1932.[3] Six months later, Gledhill and Vines won the 1933 Australian Championships doubles title.[4] In that tournament, Gledhill also recorded his best Grand Slam singles result. 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.[6]