In most operational computerized adaptive testing (CAT) programs, the Sympson-Hetter (SH) method is used to control the exposure of the items. Several modifications and improvements of the original method have been proposed. The Stocking and Lewis (1998) version of the method uses a multinomial experiment to select items. For severely constrained CAT, the list on which this experiment is conducted not only has to be of appropriate length but also needs to balance the composition of the test with respect to its specifications. In this article it is shown how the SH method of exposure control can be implemented in the shadow test approach. The method was applied to an adaptive test with 433 constraints on various attributes. Both a single and a multiple shadow-test approach were used to compare different list lengths for the SH method. (Contains 2 tables and 3 figures.)