High spin states in 113I were studied with the 58Ni(58Ni, 3pγ) reaction at 240 MeV, using the eurogam array in Daresbury, United Kingdom, with 45 Ge detectors. A total of five deformed intruder bands extending to spins I ranging from (73/2–89/2)ħ have been identified, all of which reach frequencies ħω>1.0 MeV and excitation energies ∼25 MeV. A gradual dropoff of the dynamic moment of inertia scrI (2) with increasing rotational frequency has been observed and attributed to a mode of ‘‘soft’’ band termination involving valence particle alignment. In this process, the nucleus progresses gradually, over many transitions, towards a noncollective oblate (γ=+60°) band terminating state.