This paper presents a refinement of the Bayesian Information Criterion (BIC). While the original BIC selects models on the basis of complexity and fit, the so-called prior-adapted BIC allows us to choose among statistical models that differ on three scores: fit, complexity, and model size. The prior-adapted BIC can therefore accommodate comparisons among statistical models that differ only in the admissible parameter space, e.g., for choosing among models with different constraints on the parameters. The paper ends with an application of this idea to a well-known puzzle from the psychology of reasoning, the conjunction fallacy.