Cognitive or skills diagnosis models are discrete latent variable models developed specifically for the purpose of identifying the presence or absence of multiple fine-grained skills. However, applications of these models typically involve dichotomous or dichotomized data, including data from multiple-choice (MC) assessments that are scored as right or wrong. The dichotomization approach to the analysis of MC data ignores the potential diagnostic information that can be found in the distractors and is therefore deemed diagnostically suboptimal. To maximize the diagnostic value of MC assessments, this article prescribes how MC options should be constructed to make them more cognitively diagnostic and proposes a cognitive diagnosis model for analyzing such data. The article discusses the specification of the proposed model and estimation of its parameters. Moreover, results of a simulation study evaluating the viability of the model and an estimation algorithm are presented. Finally, practical considerations concerning the proposed framework are discussed. (Contains 3 figures and 7 tables.)