Computerized adaptive tests (CATs) are individualized tests that, from a measurement point of view, are optimal for each individual, possibly under some practical conditions. In the present study, it is shown that maximum information item selection in CATs using an item bank that is calibrated with the one or the two-parameter logistic model results in each individual answering about 50% of the items correctly. Two item selection procedures giving easier (or more difficult) tests for students are presented and evaluated. Item selection on probability points of items yields good results only with the one-parameter logistic model and not with the two-parameter logistic model. An alternative selection procedure, based on maximum information at a shifted ability level, gives satisfactory results with both models. Index terms: computerized adaptive testing, item selection, item response theory