Beyond the careful design of stereo acquisition equipment and rendering algorithms, disparity post-processing has recently received much attention, where one of the key tasks is to compress the originally large disparity range to avoid viewing discomfort. The perception of dynamic stereo content however, relies on reproducing the full disparity-time volume that a scene point undergoes in motion. This volume can be strongly distorted in manipulation, which is only concerned with changing disparity at one instant in time, even if the temporal coherence of that change is maintained. We propose an optimization to preserve stereo motion of content that was subject to an arbitrary disparity manipulation, based on a perceptual model of temporal disparity changes. Furthermore, we introduce a novel 3D warping technique to create stereo image pairs that conform to this optimized disparity map. The paper concludes with perceptual studies of motion reproduction quality and task performance in a simple game, showing how our optimization can achieve both viewing comfort and faithful stereo motion.