A major issue in elementary cognition and information processing has been whether rapid search of short-term memory or a visual display can terminate when a predesignated target is found or must proceed until all items are examined. This study summarizes past and recent theoretical results on the ability of self-terminatinq and exhaustive models to predict differences in slopes between positive (target-present) and negative (target absent) set size functions, as well as position effects. The empirical literature is reviewed with regard to the presence of slope differences and position effects. Theoretical investigations demonstrate that self-terminating models can readily predict the results often associated with exhaustive Drocessing, but a very broad class of exhaustive models are incapable of predicting position effects and slope differences typically associated with self-termination. Because position effects and slope differences are found throughout the rapid search literature, we conclude that the exhaustive processing hypothesis is not tenable under common experimental conditions.