Bayesian estimation procedures are summarized and numerically illustrated by means of simulation methods. Procedures of data generation for simulation purposes are also delineated and computationally demonstrated. The logistic model basic to the Bayesian estimation procedures is shown to be explicit with respect to the probability distribution from which one is sampling. This feature allows for an assessment or evaluation of its capabilities without empirical data. The fit of the model to empirical data is discussed as an issue independent of considerations as to model capabilities. Three item banks are used to simulate Bayesian estimation procedures. Two are idealized--though reasonably possible--examples; whereas, the third consists of items specified according to other parameter estimates reported. Results indicate that with test validity held constant, Bayesian tailored testing of the Verbal Scholastic Aptitude Test (VSAT) could result in a savings of 65% of testing time for the average examinee. However, more savings in testing time is seen as possible through the use of item banks developed specifically for the purpose of tailored testing. The present investigation did not utilize prior information. Further assessments of model capabilities should explore such usage. While present results appear favorable, the full potentialities of the model have yet to be assessed. (Author/AE)