Cognitive diagnostic computerized adaptive testing (CD-CAT) can be divided into two broad categories: (a) single-purpose tests, which are based on the subject’s knowledge state (KS) alone, and (b) dual-purpose tests, which are based on both the subject’s KS and traditional ability level (). This article seeks to identify the most efficient item selection method for the latter type of CD-CAT corresponding to various conditions and various evaluation criteria, respectively, based on the reduced reparameterized unified model (RRUM) and the two-parameter logistic model of item response theory (IRT-2PLM). The Shannon entropy (SHE) and Fisher information methods were combined to produce a new synthetic item selection index, that is, the "dapperness with information (DWI)" index, which concurrently considers both KS and within one step. The new method was compared with four other methods. The results showed that, in most conditions, the new method exhibited the best performance in terms of KS estimation and the second-best performance in terms of estimation. Item utilization uniformity and computing time are also considered for all the competing methods.