Switching between two tasks afforded by the same stimuli results in slower reactions and more errors on the first stimulus after the task changes. This "switch cost" is reduced, but not usually eliminated, by the opportunity to prepare for a task switch. While there is agreement that this preparation effect indexes a control process performed before the stimulus, the "residual" cost has been attributed to several sources: to a control process essential for task-set reconfiguration that can be carried out only after the stimulus onset, to probabilistic failure to engage in preparation prior to the stimulus, and to two kinds of priming from previous trials: positive priming of the now-irrelevant task set and inhibition of the now-relevant task-set. The main evidence for the carry-over of inhibition is the observation that it is easier to switch from the stronger to the weaker of a pair of tasks afforded by the stimulus than vice versa. We survey available data on interactions between task switching and three manipulations of relative task strength: pre-experimental experience, stimulus-response compatibility, and intra-experimental practice. We conclude that it is far from universally true that it is easier to switch to the weaker task. Either inhibition of the stronger task-set is a strategy used only in the special case of extreme inequality in strength, or its consequences for later performance may be masked by slower post-stimulus control operations for more complex tasks. Inhibitory priming may also be stimulus specific.