Information based item selection methods in computerized adaptive tests (CATs) tend to choose the item that provides maximum information at an examinee's estimated trait level. As a result, these methods can yield extremely skewed item exposure distributions in which items with high "a" values may be overexposed, while those with low "a" values may never be selected. H. Chang and Z. Ying (1999) proposed the a-stratified design (ASTR) that attempts to control the exposure of high "a" items and improve the use of low "a" items simultaneously. To remedy the overexposure problem that may occur in some situations, H. Chang, J. Qian, and Z. Ying (1999) developed the a-stratified with b-blocking method (BASTR) based on ASTR. These two stratified methods have not been tested in situations where complex nonstatistical constraints are imposed. The Weighted Deviation Model (WDM) was proposed by M. Stocking and L. Swanson (1993) to deal with severely constrained item selection in CAT. An adaptation of the general ideas of the WDM to ASTR and BASTR was investigated in this study. Simulation results indicate that both ASTR and BASTR can satisfy more of the nonstatistical constraints. The BASTR outperformed the other two methods in that it effectively controlled item exposures, better used the entire pool, and substantially reduced the test-overlap rate. (Contains 3 tables, 1 figure, and 25 references.) (Author/SLD)