For computerized adaptive tests (CAT) based on the three-parameter logistic mode it was found that administering items with low discrimination parameter (a) values early in the test and administering those with high a values later was advantageous; the skewness of item exposure distributions was reduced while efficiency was maintain in trait level estimation. Thus, a new multistage adaptive testing approach is proposed that factors a into the item selection process. In this approach, the items in the item bank are stratified into a number of levels based on their a values. The early stages of a test use items with lower as and later stages use items with higher as. At each stage, items are selected according to an optimization criterion from the corresponding level. Simulation studies were performed to compare a-stratified CATs with CATs based on the Sympson-Hetter method for controlling item exposure. Results indicated that this new strategy led to tests that were well-balanced, with respect to item exposure, and efficient. The a-stratified CATs achieved a lower average exposure rate than CATs based on Bayesian or information-based item selection and the Sympson-Hetter method. (PsycINFO Database Record (c) 2003 APA, all rights reserved).