Five comparisons were made relative to the quality of estimates of ability parameters and item calibrations obtained from the one-parameter and three-parameter logistic models. The results indicate: (1) The three-parameter model fit the test data better in all cases than did the one-parameter model. For simulation data sets, multi-factor data were less well fit than single-factor data. (2) The one-parameter model ability estimates shared more variance with the item responses than did the three-parameter model. (3) There was no difference in the concurrent validity for small samples between the two models in predicting classroom achievement tests. (4) The three-parameter model required larger samples for calibration than did the one-parameter model. (5) The ability estimates from the two models correlated highly for most of the data sets. The one-parameter model is preferred for use with small sample data; but the goodness of fit data reflected a different point of view when accurate estimation of item parameters is important. The three-parameter model fit all data sets better than the one-parameter model. Data sets from the Missouri School and College Ability Tests, and from undergraduate course final examinations were used to illustrate the models. (Author/CTM)