Many psychometric measures yield data that are compatible with (a) an essentially unidimensional factor analysis solution and (b) a correlated-factor solution. Deciding which of these structures is the most appropriate and useful is of considerable importance, and various procedures have been proposed to help in this decision. The only fully developed procedures available to date, however, are internal, and they use only the information contained in the item scores. In contrast, this article proposes an external auxiliary procedure in which primary factor scores and general factor scores are related to relevant external variables. Our proposal consists of two groups of procedures. The procedures in the first group (differential validity procedures) assess the extent to which the primary factor scores relate differentially to the external variables. Procedures in the second group (incremental validity procedures) assess the extent to which the primary factor scores yield predictive validity increments with respect to the single general factor scores. Both groups of procedures are based on a second-order structural model with latent variables from which new methodological results are obtained. The functioning of the proposal is assessed by means of a simulation study, and its usefulness is illustrated with a real-data example in the personality domain.