When both visual and proprioceptive information are available about the position of a part of the body, the brain weights and combines these sources to form a single estimate, often modeled by minimum variance integration. These weights are known to vary with different circumstances, but the type of information causing the brain to change weights (reweight) is unknown. Here we studied reweighting in the context of estimating the position of a hand for the purpose of reaching it with the other hand. Subjects reached to visual (V), proprioceptive (P), or combined (VP) targets in a virtual reality setup. We calculated weights for vision and proprioception by comparing endpoints on VP reaches with endpoints on P and V reaches. Endpoint visual feedback was manipulated to control completely for the error history seen by subjects. In different experiments, we manipulated target salience, conscious effort, or statistics of the visual error history to see if these cues could cause reweighting. Most subjects could reweight strongly by conscious effort. Changes in target salience reliably caused reweighting, but seen error history alone did not. We also found that experimental weights can be predicted by minimizing the variance of visual and proprioceptive estimates, supporting the idea that minimum variance integration is an important principle of sensorimotor processing.