Estimation problems associated with the correlated-trait correlated-method (CTCM) parameterization of a multitrait-multimethod (MTMM) matrix are widely documented: the model often fails to converge; even when convergence is achieved, one or more of the parameter estimates are outside the admissible parameter space. In this study, the authors explore the potential contributions of two factors to the occurrence of nonconvergence and inadmissible solutions: (a) the minimum number of indicators per factor and (b) the deviation of the MTMM matrix from the CTCM model beyond sampling variability. Analyses of two published occupational preference data sets involving six traits and five methods and a simulation study show that the probability of obtaining problematic solutions diminishes as the minimum number of indicators per factor increases. Also, isolating factors contributing to model misfit beyond sampling variability reduces the probability of obtaining problematic solutions by one half. The implications of these findings for choosing a measurement design that improves the probability of achieving a proper solution in the analysis of an MTMM matrix using the CTCM parameterization are discussed. (Contains 1 figure.)