Although multidimensional adaptive testing (MAT) has been proven to be highly advantageous with regard to measurement efficiency when several highly correlated dimensions are measured, there are few operational assessments that use MAT. This may be due to issues of constraint management, which is more complex in MAT than it is in unidimensional adaptive testing. Very few studies have examined the performance of existing constraint management methods (CMMs) in MAT. The present article focuses on the effectiveness of two promising heuristic CMMs in MAT for varying levels of imposed constraints and for various correlations between the measured dimensions. Through a simulation study, the multidimensional maximum priority index (MMPI) and multidimensional weighted penalty model (MWPM), as an extension of the weighted penalty model, are examined with regard to measurement precision and constraint violations. The results show that both CMMs are capable of addressing complex constraints in MAT. However, measurement precision losses were found to differ between the MMPI and MWPM. While the MMPI appears to be more suitable for use in assessment situations involving few to a moderate number of constraints, the MWPM should be used when numerous constraints are involved.