There is good evidence that biological perceptual systems exploit the temporal continuity in the world: When asked to reproduce or rate sequentially presented stimuli (varying in almost any dimension), subjects typically err toward the previous stimulus, exhibiting so-called "serial dependence." At this stage it is unclear whether the serial dependence results from averaging within the perceptual system, or at later stages. Here we demonstrate that strong serial dependencies occur within both perceptual and decision processes, with very little contribution from the response. Using a technique to isolate pure perceptual effects (Fritsche, Mostert, & de Lange, 2017), we show strong serial dependence in orientation judgements, over the range of orientations where theoretical considerations predict the effects to be maximal. In a second experiment we dissociate responses from stimuli to show that serial dependence occurs only between stimuli, not responses. The results show that serial dependence is important for perception, exploiting temporal redundancies to enhance perceptual efficiency.