Two experiments examined processes underlying cognitive inflexibility in set-shifting tasks typically used to assess the development of executive function in children. Adult participants performed a Flexible Item Selection Task (FIST) that requires shifting from categorizing by one dimension (e.g., color) to categorizing by a second orthogonal dimension (e.g., shape). The experiments showed performance of the FIST involves suppression of the representation of the ignored dimension; response times for selecting a target object in an oddity task immediately following were slower when the oddity target was the previously ignored stimulus of the FIST. However, proactive interference from the previously relevant stimulus dimension also impaired responding. The results are discussed with respect to two prominent theories of the source of difficulty for children and adults on dimensional shifting tasks: "attentional inertia" and "negative priming". In contrast to prior work emphasizing one process over the other, the findings indicate that difficulty in the FIST, and by extension other set-shifting tasks, can be attributed to "both" the need to shift away from the previously attended representation ("attentional inertia") and the need to shift to the previously ignored representation ("negative priming"). Results are discussed in relation to theoretical explanations for cognitive inflexibility in adults and children. (Contains 3 figures and 1 footnote.)