An electroactive polymer actuator includes an electroactive polymer structure and a driver for providing an actuation drive signal. In one aspect, a first drive level is used to charge the electroactive polymer structure from a non-actuated state to an actuated state. When or after the electroactive polymer structure reaches the actuated state, a lower second drive level is used to hold the electroactive polymer structure at the actuated state. This temporary overdrive scheme improves the speed response without damaging the electroactive polymer structure. In another aspect, a driving method makes use of several different level segments over time, which compensates for the delayed actuation response of the EAP actuator.