We present a model and its experimental validation for the optimization of the in-plane displacement of a rigid platform mounted on a compact dielectric elastomer actuator. Unlike the situation in which the mechanical prestretch of the membrane is maintained by a dead load (which leads to the highest strain, but is unsuitable for most practical applications), we study here the case in which the dielectric membrane is stretched on a frame, with the passive zones of the membrane acting as non-linear springs, thus avoiding external weights or springs, hence allowing for a compact and simple device. We demonstrate how to maximize the displacement of the platform relative to the overall size of the device by optimum choice of membrane prestretch and electrode geometry. In particular, we show that using a passive membrane decreases the maximum displacement of the platform by a factor of 2 compared to constant-force case. However, this loss can be compensated by using bidirectional actuation, with electrodes on both sides of the platform (one side at a time serving as the passive membrane). The differences between the idealised situation of the model and manufacturable devices are discussed and validated by finite element model simulations and experimental measurements.