Perception and action are based on information from multiple sensory modalities. For instance, both vision and proprioception provide information about hand position, and this information is integrated to generate a single estimate of where the hand is in space. Classically, vision has been thought to dominate this process, with the estimate of hand position relying more on vision than on proprioception []. However, an optimal integration model [] that takes into account the precision of vision and proprioception predicts that the weighting of the two senses varies with direction and that the classical result should only hold for specific spatial directions. Using an adaptation paradigm, we show that, as predicted by this model, the visual-proprioceptive integration varies with direction. Variation with direction was so strong that, in the depth direction, the classical result was reversed: the estimate relies more on proprioception than on vision. These results provide evidence for statistically optimal integration of information from multiple modalities.