This study compared four item-selection procedures developed for use with severely constrained computerized adaptive tests (CATs). Severely constrained CATs refer to those adaptive tests that seek to meet a complex set of constraints that are often not conclusive to each other (i.e., an item may contribute to the satisfaction of several constraints at the same time). The procedures examined in the study included the weighted deviation model (WDM), the weighted penalty model (WPM), the maximum priority index (MPI), and the shadow test approach (STA). In addition, two modified versions of the MPI procedure were introduced to deal with an edge case condition that results in the item selection procedure becoming dysfunctional during a test. The results suggest that the STA worked best among all candidate methods in terms of measurement accuracy and constraint management. For the other three heuristic approaches, they did not differ significantly in measurement accuracy and constraint management at the lower bound level. However, the WPM method appears to perform considerably better in overall constraint management than either the WDM or MPI method. Limitations and future research directions were also discussed.