We compared six different analytic models for multitrait-multimethod (MTMM) data in terms of convergence, admissibility, and model fit to 258 samples of previously reported data. Two well-known models, the correlated trait-correlated method (CTCM) and the correlated trait-correlated uniqueness (CTCU) models, were fit for reference purposes in comparison to four other under- or unstudied models, including (a) Rindskopf's reparameterization of the CTCM (CTCM-R) model, (b) a correlated trait-constrained uncorrelated method model and two of its more general cases, (c) a correlated trait-constrained correlated method model, and (d) a correlated trait--uncorrelated method model. Results show that (a) the CTCM-R model often solved convergence and admissibility problems with the CTCM model at rates equivalent to the CTCU model and (b) constrained models often provided convergent and admissible solutions but significantly worse model fit, indicating that they are often not plausible when analyzing real data. A follow-up simulation study showed that the CTCM-R model also provided the most accurate estimates of the full range of parameters relevant to a confirmatory factor analytic model of MTMM data.