We investigated whether humans use a target's remembered location to plan reaching movements to targets according to the relative reliabilities of visual and remembered information. Using their index finger, subjects moved a virtual object from one side of a table to the other, and then went back to a target. In some trials, the target shifted unnoticed while the finger made the first movement. We regressed subjects' movement trajectories against the initial and shifted target locations to infer the weights that subjects gave to remembered and visual locations. We measured the reliability of vision and memory by adding conditions in which the target only appeared after subjects made the first movement (vision only) and in which the target was initially present but disappeared during the first movement (memory only). When both visual and remembered information were available, movement trajectories were biased to the remembered target location. The different weights that subjects gave to memory and visual information on average matched the weights predicted by the variance associated with the use of vision and memory alone. This suggests that humans integrate remembered information about object locations with peripheral visual information by taking into account the relative reliability of the two sources of information.