Notes that in computerized adaptive testing (CAT), a examinee's trait level (θ) must be estimated with reasonable accuracy based on a small number of item responses. A successful implementation of CAT depends on (1) the accuracy of statistical methods used for estimating θ and (2) the efficiency of the item-selection criterion. Methods of estimating θ suitable for CAT are reviewed, and the differences between Fisher and Kullback-Leibler information criteria for selecting items are discussed. The accuracy of different CAT algorithms was examined in an empirical study. The results show that correcting θ estimates for bias was necessary at earlier stages of CAT, but most CAT algorithms performed equally well for tests of 10 or more items. (PsycINFO Database Record (c) 2005 APA )