The models of standard test theory, having evolved under a trait-oriented psychology, do not reflect the knowledge structures and the problem-solving strategies now seen as central to understanding performance and learning. In some applications, however, key qualitative distinctions among persons as to structures and strategies can be expressed through mixtures of test theory models, drawing upon substantive theory to delineate the components of the mixture. This approach is illustrated with response latencies to spatial visualization tasks that can be solved by mental rotation or by a nonspatial rule-based strategy. It is assumed that a subject employs the same strategy on all tasks, but the possibility of extending the approach to strategy-switching is discussed. (Contains 21 references, 8 tables, and 6 figures.) (Author)