Fixed-precision between-item multidimensional computerized adaptive tests (MCATs) are becoming increasingly popular. The current generation of item-selection rules used in these types of MCATs typically optimize a single-valued objective criterion for multivariate precision (e.g., Fisher information volume). In contrast, when all dimensions are of interest, the stopping rule is typically defined in terms of a required fixed marginal precision per dimension. This asymmetry between multivariate precision for selection and marginal precision for stopping, which is not present in unidimensional computerized adaptive tests, has received little attention thus far. In this article, we will discuss this selection-stopping asymmetry and its consequences, and introduce and evaluate three alternative item-selection approaches. These alternatives are computationally inexpensive, easy to communicate and implement, and result in effective fixed-marginal-precision MCATs that are shorter in test length than with the current generation of item-selection approaches.