The Monte Carlo approach which has previously been implemented in traditional computerized adaptive testing (CAT) is applied here to cognitive diagnostic CAT to test the ability of this approach to address multiple content constraints. The performance of the Monte Carlo approach is compared with the performance of the modified maximum global discrimination index (MMGDI) method on simulations in which the only content constraint is on the number of items that measure each attribute. The results of the two simulation experiments show that (a) the Monte Carlo method fulfills all the test requirements and produces satisfactory measurement precision and item exposure results and (b) the Monte Carlo method outperforms the MMGDI method when the Monte Carlo method applies either the posterior-weighted Kullback-Leibler algorithm or the hybrid Kullback-Leibler information as the item selection index. Overall, the recovery rate of the knowledge states, the distribution of the item exposure, and the utilization rate of the item bank are improved when the Monte Carlo method is used.