During the early stage of computerized adaptive testing (CAT), item selection criteria based on Fisher"s information often produce less stable latent trait estimates than the Kullback-Leibler global information criterion. Robustness against early stage instability has been reported for the D-optimality criterion in a polytomous CAT with the Nominal Response Model and is shown herein to be reproducible for the Graded Response Model. For comparative purposes, the A-optimality and the global information criteria are also applied. Their item selection is investigated as a function of test progression and item bank composition. The results indicate how the selection of specific item parameters underlies the criteria performances evaluated via accuracy and precision of estimation. In addition, the criteria item exposure rates are compared, without the use of any exposure controlling measure. On the account of stability, precision, accuracy, numerical simplicity, and less evidently, item exposure rate, the D-optimality criterion can be recommended for CAT. (Contains 9 figures and 1 table.)