The eyes are in continuous motion. A robust system required to make spatial separation judgments should be resistant to the positional noise produced by such movements. Two parallel lines have been jittered horizontally in order to assess the impact of stimulus movement on the retina. Jitter that maintains the separation between the two lines has minimal effect on separation discrimination thresholds, regardless of whether the targets in the two eyes jitter in a positively correlated, negatively correlated or uncorrelated manner. Presenting both eyes with line pairs but only altering the separation in one eye in the second interval yields poorer performance. However, if one eye receives a change in separation while the other views a dark screen then that monocular threshold is very similar to the binocular threshold. These results are most simply explained by procedures which average the monocular separation estimates.