Differences of less than 20 sec of visual angle in the separation of a pair of closely spaced parallel lines can be reliably detected. This ability is known as a hyperacuity because the thresholds are smaller than the diameter of one foveal cone. It is shown that this ability does not require a stationary pattern. Indeed, correlated horizontal jitter of the line pair has little detrimental effect on performance for jitter that ranges up to 8 min arc for two lines with a separation of only 6 min arc. Uncorrelated jitter of the two lines, which allows the actual separation to vary from moment to moment, causes performance to deteriorate at a rate similar to the rise of signal uncertainty. The results reflect the operation of a system which is not only extremely robust to oculomotor instability but is also robust to positional variation that could not be produced by eye movements.