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The performance overhead associated with changing tasks (the “switch cost”) usually diminishes when the task is specified in advance but is rarely eliminated by preparation. A popular account of the “residual” (asymptotic) switch cost is that it reflects “task-set inertia”: carry-over of task-set parameters from the preceding trial(s). New evidence for a component of “task-set inertia” comes from eye-tracking, where the location associated with the previously (but no longer) relevant task is fixated preferentially over other irrelevant locations, even when preparation intervals are generous. Might such limits in overcoming task-set inertia in general, and “attentional inertia” in particular, result from suboptimal scheduling of preparation when the time available is outside one’s control? In the present study, the stimulus comprised 3 digits located at the points of an invisible triangle, preceded by a central verbal cue specifying which of 3 classification tasks to perform, each consistently applied to just 1 digit location. The digits were presented only when fixation moved away from the cue, thus giving the participant control over preparation time. In contrast to our previous research with experimenter-determined preparation intervals, we found no sign of attentional inertia for the long preparation intervals. Self-paced preparation reduced but did not eliminate the performance switch cost—leaving a clear residual component in both reaction time and error rates. That the scheduling of preparation accounts for some, but not all, components of the residual switch cost, challenges existing accounts of the switch cost, even those which distinguish between preparatory and poststimulus reconfiguration processes.