According to the assumption of monotonicity in similarity judgments, adding a shared feature in common to two items should increase or leave unchanged, but should never decrease, their similarity. Violations of monotonicity are not predicted by feature- or dimension-based models, but can be accommodated by alignment-based models. According to alignment-based models, when structured displays are compared, the parts of one compared display must be aligned, or placed in correspondence with the parts of the other display. In two experiments, evidence for nonmonotonicities is obtained that is generally, although not entirely, consistent with the alignment-based model SIAM (Similarity as Interactive Activation and Mapping; Goldstone, 1994). The primary assumption of the model is that the calculation of similarity involves an interactive activation process whereby correspondences between the parts of compared displays mutually and concurrently influence each other. As SIAM predicts, the occurrence of nonmonotonicities depends on the perceptual similarity of features and the duration of presented comparisons.