The multitrait-multimethod (MTMM) paradigm is used widely to assess construct validity, but D. A. Kenny and D. A. Kashy (1992) lament that even after 30 years we still do not know how to analyze MTMM data. The Composite Direct Product (CDP) model has recently attracted considerable attention. Its strengths and weaknesses are evaluated, and a stronger basis for testing the model is demonstrated. The CDP model is mathematically elegant and extremely parsimonious, but this parsimony is at the expense of very restrictive assumptions that undermine the formative evaluation of MTMM data. Furthermore, the CDP model provides an excellent fit to simulated data in which these assumptions are seriously violated, demonstrating that fit is not a sufficient test of these assumptions. Typically the CDP model is based on single indicators of each trait/method combination, but a stronger multiple-indicator version of the CDP model is demonstrated using new options available in the LISREL 8 computer program. Five tables present data illustrating the CDP model, using data from a study by B. M. Bryne and R. J. Shavelson (1986) on the relations among three academic self-concept traits. An appendix presents a LISREL setup for fitting the multiple indicator CDP model. (SLD)