An electronic lockbox uses a rotary actuator with multiple positions to achieve multiple locking states. Multiple positions of the actuator are detected, using optical sensors. The locking mechanism includes an outer sleeve and an inner cylindrical barrel that are coupled with torsion springs. The lockbox has a shackle and a key bin that are retained by the inner barrel when in the locked state, and the barrel can be rotated to either release the shackle or to release the key bin that typically holds a building's key.