Visual perception is strongly influenced by contextual information. A good example is reference repulsion, where subjective reports about the direction of motion of a stimulus are significantly biased by the presence of an explicit reference. These perceptual biases could arise early, during sensory encoding, or alternatively, they may reflect decision-related processes occurring relatively late in the task sequence. To separate these two competing possibilities, we asked (human) subjects to perform a fine motion-discrimination task and then estimate the direction of motion in the presence or absence of an oriented reference line. When subjects performed the discrimination task with the reference, but subsequently estimated motion direction in its absence, direction estimates were unbiased. However, when subjects viewed the same stimuli but performed the estimation task only, with the orientation of the reference line jittered on every trial, the directions estimated by subjects were biased and yoked to the orientation of the shifted reference line. These results show that judgements made relative to a reference are subject to late, decision-related biases. A model in which information about motion is integrated with that of an explicit reference cue, resulting in a late, decision-related re-weighting of the sensory representation, can account for these results.