Created random-dot cinematograms in which each dot's successive movements were independently drawn from a Gaussian distribution of directions of some characteristic bandwidth. Using pairs of cinematograms, direction discrimination of global motion was measured in 4 undergraduates and 1 of the present authors under various conditions of direction distribution bandwidth, exposure and duration, and constancy of each dot's path. A line-element model accounted for the results. Over a considerable range, discrimination was unaffected by the cinematogram's direction distribution bandwidth. Only for the briefest presentations did changes in duration have an effect. So long as the overall directional content of the cinematogram remained unchanged, the constancy or randomness of individual dots' paths did not affect discrimination.