People often prefer simpler explanations because they have higher prior probability. However, simpler explanations are not always normatively superior because they often do not fit the data as well as complex explanations. How do people negotiate this trade-off between prior probability (favoring simplicity) and goodness-of-fit (favoring complexity)? Here, we argue that people use opponent heuristics—relying on simplicity as a cue to prior probability but complexity as a cue to goodness-of-fit (Study 1). We also examine factors that lead one or the other heuristic to predominate in a given context. Study 2 finds that people have a stronger simplicity preference in deterministic rather than stochastic contexts, while Study 3 finds that people have a stronger simplicity preference for physical rather than social causal systems. Together, we argue that these cues and contextual moderators act as powerful constraints that help to specify otherwise ill-defined hypothesis comparison problems.