Dielectric elastomer actuators (DEAs) are an attractive form of electromechanical transducer, possessing high energy densities, an efficient design, mechanical flexibility, high speed, and noiseless operation. They have been incorporated into a variety of elegant devices, such as microfluidic devices, tunable optics, haptic displays, and minimum-energy grippers. Dielectric elastomer minimum energy structures (DEMESs) take advantage of the prestretch of the DEA to bend a non-stretchable but flexible component to perform mechanical work. The gripper is perhaps the most intuitive type of DEMES, capable of grasping objects but with only small to moderate forces. We present a novel configuration of a DEA using electrodes made of a conductive shape-memory polymer (SMP), incorporated into the design of a gripper. The SMP electrodes allow the DEA to be rigid in the cold state, offering greater holding force than a conventional gripper. Joule heating applied to the SMP electrodes softens them, allowing for electrostatic actuation. Cooling then locks in the actuated position without the need for continued power to be supplied. Additionally, the Joule heating voltage is at least one order of magnitude less than electrostatic actuation voltages, allowing for addressing of multiple actuator elements using commercially available transistors. The shape memory gripper incorporates this addressing into its design, enabling the three segments of each finger to be controlled independently.