The extensive computer simulation work done in developing the computer adaptive versions of the Graduate Record Examinations (GRE) Board General Test and the College Board Admissions Testing Program (ATP) Scholastic Aptitude Test (SAT) is described in this report. Both the GRE General and SAT computer adaptive tests (CATs), which are fixed length in nature, were developed from pools of items that were calibrated using the three-parameter item response theory model, and item selection was based on the recently developed weighted deviations algorithm (see Swanson and Stocking, 1992), which simultaneously deals with content, statistical, and other constraints in the item selection process. For the GRE General CATs (Verbal, Quantitative, and Analytical), item exposure was controlled by using an extension of an approach originally developed by Sympson and Hetter (1988). For the SAT CATs (Verbal and Mathematical), item exposure was controlled by using a less complex randomization approach. Lengths of the CATs were determined so that CAT reliabilities matched or exceeded comparable full length paper-and-pencil test reliabilities. Eight figures and 23 tables illustrate the analysis. (Contains 21 references.) (Author/SLD)