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For item selection in cognitive diagnostic computerized adaptive testing (CD-CAT), ideally, a single item selection index should be created to simultaneously regulate precision, exposure status, and attribute balancing. For this purpose, in this study, we first proposed an attribute-balanced item selection criterion, namely, the standardized weighted deviation global discrimination index (SWDGDI), and subsequently formulated the constrained progressive index (CP_SWDGDI) by casting the SWDGDI in a progressive algorithm. A simulation study revealed that the SWDGDI method was effective in balancing attribute coverage and the CP_SWDGDI method was able to simultaneously balance attribute coverage and item pool usage while maintaining acceptable estimation precision. This research also demonstrates the advantage of a relatively low number of attributes in CD-CAT applications. [ABSTRACT FROM AUTHOR]