Recent years have seen a boom in interest in machine learning systems that can provide a human-understandable rationale for their predictions or decisions. However, exactly what kinds of explanation are truly human-interpretable remains poorly understood. This work advances our understanding of what makes explanations interpretable under three specific tasks that users may perform with machine learning systems: simulation of the response, verification of a suggested response, and determining whether the correctness of a suggested response changes under a change to the inputs. Through carefully controlled human-subject experiments, we identify regularizers that can be used to optimize for the interpretability of machine learning systems. Our results show that the type of complexity matters: cognitive chunks (newly defined concepts) affect performance more than variable repetitions, and these trends are consistent across tasks and domains. This suggests that there may exist some common design principles for explanation systems.