Many recent advances in deep learning for natural language processing have come at increasing computational cost, but the power of these state-of-the-art models is not needed for every example in a dataset. We demonstrate two approaches to reducing unnecessary computation in cases where a fast but weak baseline classier and a stronger, slower model are both available. Applying an AUC-based metric to the task of sentiment classification, we find significant efficiency gains with both a probability-threshold method for reducing computational cost and one that uses a secondary decision network.