In computerized adaptive testing (CAT), traditionally the most discriminating items are selected to provide the maximum information so as to attain the highest efficiency in trait (theta) estimation. The maximum information (MI) approach typically results in unbalanced item exposure and hence high item-overlap rates across examinees. Recently, Yi and Chang (2003) proposed the multiple stratification (MS) method to remedy the shortcomings of MI. In MS, items are first sorted according to content, then difficulty and finally discrimination parameters. As discriminating items are used strategically, MS offers a better utilization of the entire item pool. However, for testing with imposed non-statistical constraints, this new stratification approach may not maintain its high efficiency. Through a series of simulation studies, this research explored the possible benefits of a mixture item selection approach (MS-MI), integrating the MS and MI approaches, in testing with non-statistical constraints. In all simulation conditions, MS consistently outperformed the other two competing approaches in item pool utilization, while the MS-MI and the MI approaches yielded higher measurement efficiency and offered better conformity to the constraints. Furthermore, the MS-MI approach was shown to perform better than MI on all evaluation criteria when control of item exposure was imposed.