This study explored a computerized adaptive test delivery algorithm for latent class identification based on the mixture Rasch model. Four item selection methods based on the Kullback–Leibler (KL) information were proposed and compared with the reversed and the adaptive KL information under simulated testing conditions. When item separation was large, all item selection methods did not differ evidently in terms of accuracy in classifying examinees into different latent classes and estimating latent ability. However, when item separation was small, two methods with class-specific ability estimates performed better than the other two methods based on a single latent ability estimate across all latent classes. The three types of KL information distributions were compared. The KL and the reversed KL information could be the same or different depending on the ability level and the item difficulty difference between latent classes. Although the KL information and the reversed KL information were different at some ability levels and item difficulty difference levels, the use of the KL, the reversed KL, or the adaptive KL information did not affect the results substantially due to the symmetric distribution of item difficulty differences between latent classes in the simulated item pools. Item pool usage and classification convergence points were examined as well.