Large-field visual motion elicits tracking eye movements at ultra-short latency, often termed ocular following responses (OFRs). We recorded the initial OFRs of three human subjects when vertical sine-wave gratings were subject to horizontal motion in the form of successive 1/4-wavelength steps. The gratings could occupy the full screen (45 degrees wide, 30 degrees high) or a number of horizontal strips, each 1 degrees high and extending the full width of the display. These strips were always equally spaced vertically. In a first experiment, the gratings always had a contrast of 32%. Increasing the number of strips could reduce the response latency by up to 20 ms, so the magnitude of the initial OFRs was estimated from the change in eye position over the initial open-loop period measured with respect to response onset. A single (centred) strip (covering 3.3% of the screen) always elicited robust OFRs, and three strips (10% coverage) were sufficient to elicit the maximum OFR. Increasing the number of strips to 15 (50% coverage) had little impact, i.e., responses had asymptoted, and further increasing the coverage to 100% (full screen image) actually decreased the OFR so that it was now less than that elicited with only one strip. In a second experiment, the contrast of the gratings could be fixed at one of the four levels ranging from 8% to 64%, and the OFR showed essentially the same pattern of dependence on screen coverage except that the lower the contrast, the lower the level at which the response asymptoted. This indicated that the asymptote was not due simply to some upper limit on the magnitude of the eye movement or the underlying motion signals. We postulate that this asymptote is the result of normalization due to global divisive inhibition, which has often been described in visual-motion-selective neurons in the cortex. We further suggest that the decrease in the OFR when the image filled the screen was due to the increased continuity of the gratings which we postulate would favour the local inhibitory surround mechanisms over the central excitatory ones. This study indicates that robust OFRs can be elicited by much smaller motion stimuli than is commonly supposed and that introducing spatial discontinuities can increase the efficacy of the motion stimuli even while decreasing the area stimulated.