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This dissertation aimed to evaluate the performance of the multinomial extension of expected Shannon Entropy compared to two new item selection methods for CD-CAT based on theoretical correct classification rates, along with a random fixed form, and a well-designed fixed form using four different evaluation measures. These methods were evaluated using the attribute-level correct classification rates across all attributes and examinees and attribute profile CCRs, as well as calculating the proportion of items exposed in each item bank, the average absolute deviation of the posterior probabilities from 0.5, and the average time. This study was fully crossed across three conditions: number of attributes, test length, and the quality of the item bank. Consistent with prior research, a key finding was that each of the CD-CAT methods performed similarly, with no more than a 10% improvement when compared to a randomly constructed fixed form test, with a smaller gap in improvement compared to the well-designed fixed form. The multinomial extension of expected Shannon Entropy performed better than the single attribute and composite attribute theoretical CCR methods, as well as both fixed form methods across all measures. Due to the high computational demand of the multinomial extension of expected Shannon Entropy, the composite attribute theoretical CCR method is a more efficient choice for balancing performance and time. Recommendations were discussed for future research to vary more conditions to have broader applications to real data and assessments.