Similarity underlies fundamental cognitive capabilities such as memory, categorization, decision making, problem solving, and reasoning. Although recent approaches to similarity appreciate the structure of mental representations, they differ in the processes posited to operate over these representations. We present an experiment that differentiates among extant structural accounts of similarity in their ability to account for patterns of similarity ratings. These data pose a challenge for transformation-based models and all but one mapping-based model, the Similarity as Interactive Activation and Mapping (SIAM) model of similarity.