Discrete sequences of sampled motion often appear flickering and jerky. We present evidence showing that a target in sampled motion is perceived as smoother when structure in the background appears and disappears synchronously with the target. Specifically, we found that target flicker is turned into permanent target visibility at short interstimulus intervals and jerkiness is replaced by smoothly accelerating and decelerating motion at longer ones. We argue that this "smoothening" effect is essentially a form of amodal completion in space-time being evoked by spatiotemporal cues to occlusion. The effect highlights the importance of amodal representations in perception.