Nematic liquid crystal spatial light modulators (SLMs) with fast switching times and high diffraction efficiency are important to various applications ranging from optical beam steering and adaptive optics to optical tweezers. Here we demonstrate the great benefits that can be derived in terms of speed enhancement without loss of diffraction efficiency from two mutually compatible approaches. The first technique involves the idea of overdrive, that is the calculation of intermediate patterns to speed up the transition to the target phase pattern. The second concerns optimization of the target pattern to reduce the required phase change applied to each pixel, which in addition leads to a substantial reduction of variations in the intensity of the diffracted light during the transition. When these methods are applied together, we observe transition times for the diffracted light fields of about 1 ms, which represents up to a tenfold improvement over current approaches. We experimentally demonstrate the improvements of the approach for applications such as holographic image projection, beam steering and switching, and real-time control loops.