Smooth pursuit eye movements are guided largely by retinal-image motion. To compensate for neural conduction delays, the brain employs a predictive mechanism to generate anticipatory pursuit that precedes target motion (E. Kowler, 1990). A critical question for interpreting neural signals recorded during pursuit concerns how this mechanism is interfaced with sensorimotor processing. It has been shown that the predictor is not simply turned-off during randomization because anticipatory eye velocity remains when target velocity is randomized (E. Kowler & S. McKee, 1987; G. W. Kao & M. J. Morrow, 1994). This study was completed to compare pursuit behavior during randomized motion-onset timing with that occurring during direction or speed randomization. We found that anticipatory eye velocity persisted despite motion-onset randomization, and that anticipation onset time was between that observed in the different constant-timing conditions. This centering strategy was similar to the bias of eye velocity magnitude away from extremes observed when direction or speed was randomized. Such a strategy is comparable to least-squares error minimization, and could be used to facilitate acquisition of a target when it begins to move. Centering was in some observers accounted for by a shift of eye velocity toward that generated in the preceding trial. The results make unlikely a model in which the predictor is disengaged by randomizing stimulus timing, and suggest that predictive signals always interact with those used in sensorimotor processing during smooth pursuit.