A model for constrained computerized adaptive testing is proposed in which the information in the test at the ability estimate is maximized subject to a large variety of possible constraints on the contents of the test. At each item-selection step, a full test is first assembled to have maximum information at the current ability estimate fixing the items previously administered. Then the item with maximum information is selected from the test. All test assembly is optimal due to the use of a linear programming model that is automatically updated to allow for the attributes of items already administered as well as the new value of the ability estimator. A simulation study using a pool of 753 items from the Law School Admission Test (LSAT) showed that for adaptive tests of realistic lengths the ability estimator did not suffer any loss of efficiency from the presence of 433 constraints on the item selection process. (Contains 3 tables, 2 figures, and 35 references.) (Author/SLD)