Profile similarity indices (PSIs) have become widely used in studies of congruence (i.e., fit, matching, similarity, agreement) in organizational research. PSIs combine two sets of measures, or profiles, from corresponding entities (e.g., the person and organization, supervisor and subordinate, organization and environment) into a single score intended to represent their overall congruence. Unfortunately, PSIs are conceptually ambiguous, discard information essential to testing congruence hypotheses, conceal the source of the difference between entities, and impose a highly restrictive set of constraints on the coefficients relating the measures comprising the PSI to the outcome. This article shows how polynomial regression analysis may be used to avoid problems with PSIs while capturing the underlying relationships PSIs are intended to represent. Limitations and extensions to the procedure are discussed.