This paper uses recent advances in Bayesian estimation methods to exploit fully and efficiently the time-series and cross-sectional empirical restrictions of the Cox, Ingersoll, and Ross model of the term structure. We examine the extent to which the cross-sectional data (five different instruments) provide information about the model. We find that the time-series restrictions of the two-factor model are generally consistent with the data. However, the model's cross-sectional restrictions are not. We show that adding a third factor produces a significant statistical improvement, but causes the average time-series fit to the yields themselves to deteriorate.