1. Binocular discrimination of the direction of a target's motion in depth was measured in terms of the smallest angular difference in direction that could be detected with a probability 50% better than chance. Directional discrimination was measured for targets moving along 16 different trajectories directed to the left and right of the nose. 2. The relative velocities of the retinal images in the left and right eyes gave a sensitive cue to the direction of the target's motion in depth. 3. The direction of motion was bets discriminated when the target moved along a line directed close to the nose. A change in direction of only 0.2 degrees from this direction of motion could be detected. Discrimination showed two other maxima, one on each side of the central maximum. Discrimination fell to about 0.6-0.8 degrees when the target's direction was changed by only 6 degrees to either side of the nose. 4. The curve of sensitivity to movement in depth had a generally inverse shape to the directional discrimination curve: sensitivity was minimal for trajectories directed near the nose and increased for trajectories directed so as to miss the head. 5. The directional discrimination curve can be related to the sensitivity curves of the four postulated neural mechanisms tuned to different directions of motion in depth; there are three discrimination maxima and, correspondingly, three trajectories for which the slopes of adjacent sensitivity curves differ maximally. This suggests that binocular psychophysical judgements of the direction along which a target moves in depth are to some extent mediated by neural mechanisms that compare (e.g. subtract) the outputs of directionally tuned movement detectors. One function of such neural comparators might be to enhance psychophysical sensitivity to the direction along which a target moves in depth, and thus to provide a physiological basis for precisely judging whether or not an object will hit the head. 6. We suggest that the neural basis for judging the direction of moving objects has an analogy in colour vision where opponent-colour mechanisms enhance sensitivity to wave-length differences in such a way that wave-lengths are more easily discriminated in those parts of the spectrum where the slopes of the pigment action spectra differ maximally.