This article presents a new algorithm for computerized adaptive testing (CAT) when content constraints are present. The algorithm is based on shadow CAT methodology to meet content constraints but applies Monte Carlo methods and provides the following advantages over shadow CAT: (a) lower maximum item exposure rates, (b) higher utilization of the item pool, and (c) more robust ability estimates. Computer simulations with Law School Admission Test items demonstrated that the new algorithm (a) produces similar ability estimates as shadow CAT but with half the maximum item exposure rate and 100% pool utilization and (b) produces more robust estimates when a high- (or low-) ability examinee performs poorly (or well) at the beginning of the test. (Contains 6 figures.)