Under carefully controlled conditions, in blocks of trials in which the stimulus displacement on any given trial is randomly selected from a group of two, four, or eight possible displacements, latency for lateral saccadic eye movement does not change. Moreover, a subject trained on such a disjunctive latency task, and then presented with blocks of trials in which there is only one possible stimulus displacement, of probability 1.00, 0.75, 0.50, or 0.25, displays the same latency to that displacement as when it was embedded in one of the disjunctive sets. These results conflict with reports that knowledge of stimulus location determines saccade latency. When the saccade on each trial is under the control of the stimulus on that trial, the size of the set of possible stimulus displacements does not affect latency to a particular displacement. These results also suggest that previous estimates of saccade latency using single stimulus displacements were underestimates, because subjects were not trained to follow stimulus displacement in a disjunctive task. Care is required if saccade latencies are to be entirely attributed to control by stimulus factors.