Lien, Ruthruff, Remington, & Johnston (2005) reported residual switch cost differences between stimulus-response (S-R) pairs and proposed the partial-mapping preparation (PMP) hypothesis, which states that advance preparation will typically be limited to a subset of S-R pairs because of structural capacity limitations, to account for these differences. Alternatively, the failure-to-engage (FTE) hypothesis does not allow for differences in probability of advance preparation between S-R pairs within a set; it accounts for residual switch cost differences by assuming that benefits of advance preparation may differ between S-R pairs. Three Experiments were designed to test between these hypotheses. No capacity limitations of the type assumed by the PMP hypothesis were found for many participants in Experiment 1. In Experiments 2 and 3, no evidence was found for the dependency of residual switch cost differences between S-R pairs on response-stimulus interval that is predicted by the PMP hypothesis. Mixture-model analysis of reaction times distributions in Experiment 3 provided strong support for the FTE hypothesis over the PMP hypothesis. Simulation studies with a computational implementation of the FTE hypothesis showed that it is able to account in great detail for the results of the present study. Together, these results provide strong evidence against the PMP hypothesis and support the FTE hypothesis that advance preparation probabilistically fails or succeeds at the level of the task set. (Contains 3 footnotes, 2 tables, and 6 figures.)