We address a surprising result in a previous study of speed discrimination with multiple moving gratings: discrimination thresholds decreased when the number of stimuli was increased, but remained unchanged when the area of a single stimulus was increased [Verghese & Stone (1995). Vision Research, 35, 2811-2823]. In this study, we manipulated the spatial- and phase relationship between multiple grating patches to determine their effect on speed discrimination thresholds. In a fusion experiment, we merged multiple stimulus patches, in stages, into a single patch. Thresholds increased as the patches were brought closer and their phase relationship was adjusted to be consistent with a single patch. Thresholds increased further still as these patches were fused into a single patch. In a fission experiment, we divided a single large patch into multiple patches by superimposing a cross with luminance equal to that of the background. Thresholds decreased as the large patch was divided into quadrants and decreased further as the quadrants were maximally separated. However, when the cross luminance was darker than the background, it was perceived as an occluder and thresholds, on average, were unchanged from that for the single large patch. A control experiment shows that the observed trend in discrimination thresholds is not due to the differences in perceived speed of the stimuli. These results suggest that the parsing of the visual image into entities affects the combination of speed information across space, and that each discrete entity effectively provides a single independent estimate of speed.