Several alternatives for item selection algorithms based on item response theory in computerized classification testing (CCT) have been suggested, with no conclusive evidence on the substantial superiority of a single method. It is argued that the lack of sizable effect is because some of the methods actually assess items very similarly through different calculations and will usually select the same item. Consideration of methods that assess information across a wider range is often unnecessary under realistic conditions, although it might be advantageous to utilize them only early in a test. In addition, the efficiency of item selection approaches depend on the termination criteria that are used, which is demonstrated through didactic example and Monte Carlo simulation. Item selection at the cut score, which seems conceptually appropriate for CCT, is not always the most efficient option. A broad framework for item selection in CCT is presented that incorporates these points. (Contains 1 figure and 6 tables.)