Discriminating between two speed signals is harder when they are seen as part of a single trajectory, compared to the case when they appear as distinct entities. Observers were asked to judge which half of a display had dots that were moving faster. This was done under two main conditions: when dot motion appeared to continue across the boundary between the two halves, and when it moved parallel to the boundary. Speed discrimination thresholds were elevated when motion in the two halves appeared to cross the boundary compared to the case when motion was parallel to the boundary. Extensive practice improved performance until speed discrimination in the two cases was virtually indistinguishable. The addition of noise caused the original effect to reappear, i.e., thresholds were elevated when motion continued across the border. Our results suggest that the local differences in velocity on either side of border are ignored when motion appears to cross the border. Instead the visual system seems to enforce an a priori assumption that when motion continues across a boundary it belongs to a common motion path.