Whittaker, Chang, and Dodd compared the performance of model selection criteria when selecting among mixed-format IRT models and found that the criteria did not perform adequately when selecting the more parameterized models. It was suggested by M. S. Johnson that the problems when selecting the more parameterized models may be because of the low variance of the discrimination parameters used to generate the data. This simulation study reproduced the Whittaker et al. study by incorporating more variability in the discrimination parameter estimates used to generate the data. The results indicated that the majority of the criteria performed more accurately when selecting the more parameterized models. Differences among the criteria performance under certain conditions and implications for model selection practice are discussed.