One generally has the impression that one feels one's hand at the same location as one sees it. However, because our brain deals with possibly conflicting visual and proprioceptive information about hand position by combining it into an optimal estimate of the hand's location, mutual calibration is not necessary to achieve such a coherent percept. Does sensory integration nevertheless entail sensory calibration? We asked subjects to move their hand between visual targets. Blocks of trials without any visual feedback about their hand's position were alternated with blocks with veridical visual feedback. Whenever vision was removed, individual subjects' hands slowly drifted toward the same position to which they had drifted on previous blocks without visual feedback. The time course of the observed drift depended in a predictable manner (assuming optimal sensory combination) on the variable errors in the blocks with and without visual feedback. We conclude that the optimal use of unaligned sensory information, rather than changes within either of the senses or an accumulation of execution errors, is the cause of the frequently observed movement drift. The conclusion that seeing one's hand does not lead to an alignment between vision and proprioception has important consequences for the interpretation of previous work on visuomotor adaptation.