Fit of the model to the data is important if the benefits of item response theory (IRT) are to be obtained. In this study, the authors compared model selection results using the likelihood ratio test, two information-based criteria, and two Bayesian methods. An example illustrated the potential for inconsistency in model selection depending on which of the indices was used. Results from a simulation study indicated that the inconsistencies among the indices were common but that model selection was relatively accurate for longer tests administered to larger sample of examinees. The cross-validation log-likelihood (CVLL) appeared to work the best of the five models for the conditions simulated in this study. The following are appended: (1) WinBUGS Code Used for Three-Parameter Logistic (3PM) Model; and (2) MATLAB Code Used for Calculating Cross-Validation Log-Likelihood (CVLL). (Contains 9 tables and 3 figures.)