For any given location and velocity of a point target, there are infinitely many different eye velocities that the pursuit system could use to track the target perfectly. Three-dimensional recordings of eye position and velocity in 8 normal human subjects showed that the system chooses the unique tracking velocity that keeps eye position vectors (a particular mathematical representation of three-dimensional eye orientation) confined to a single plane, i.e. pursuit obeys Listing's law. One advantage of this strategy over other possible ones, such as choosing the smallest eye velocity compatible with perfect tracking, is that it permits continuous pursuit without accumulation of ocular torsion. For nonpoint targets, there is at most one eye velocity compatible with perfect retinal image stabilisation, and the optimal velocity may not fit Listing's law; we observed small but consistent deviations from the law during pursuit of rotating line targets.