Properties of the collective bands in 125I, populated in 123Sb(α,2nγ)125I reaction at E=30 MeV, have been studied from γ-ray angular distributions and excitation functions. Spins and parities are inferred for several states. New E2/M1 mixing ratios are deduced for five transitions. A three-quasiparticle collective band is proposed on the basis of these and earlier results. The shapes of the ground state yrast band and the g9/2 band are discussed, providing evidence for the coexistence of prolate and oblate collective states.