Proton–gamma coincidences from the reaction 32S(α,pγ)35Cl at Eα = 10.975, 11.960, and 12.120 MeV have been measured, using method II of Litherland and Ferguson. Twelve previously unreported levels between 3.94 and 6.40 MeV excitation energy have been found. The spins of four levels, 1.763 (5/2), 2.646 (7/2), 3.945 (9/2), and 4.885 (7/2), have been determined. Possible spins have been assigned to 12 of the other levels. Branching ratios and γ-ray multipole mixing ratios for all the levels studied are given.