This study applied the maximum expected information (MEI) and the maximum posterior-weighted information (MPI) approaches of computer adaptive testing item selection to the case of a test using polytomous items following the partial credit model. The MEI and MPI approaches are described. A simulation study compared the efficiency of ability estimation using the MEI and MPI approaches to the traditional maximal item information (MII) approach. The results of the simulation study indicated that the MEI and MPI approaches led to a superior efficiency of ability estimation compared with the MII approach. The superiority of the MEI and MPI approaches over the MII approach was greatest when the bank contained items having a relatively peaked information function.