The threshold stimulus for visual motion discrimination was analyzed into the constituent parameters of velocity, i.e., time and distance, with both of these primary variables subject-determined. It was found that, given a constant stimulus luminance, motion threshold was characterized generally by a “trade-off” or inverse power relationship between time and distance of movement. Earlier reports of energy constancy at threshold (R. H. Brown, 1955, 1957, 1958), implying threshold relationships incompatible with these, were confirmed only for the atypical conditions of high-velocity/low-Iuminance stimuli and were attributed to absolute visibility requirements. Under more general and representative conditions, threshold was relatively insensitive to luminance. The present results were also contrasted with earlier findings (Graham. 1968) of distance or “displacement” constancy at threshold, pertaining to movement between stationary start and stop positions.