Purpose The purpose of this paper is to introduce the reader to the nature of confirmatory bifactor modelling. Confirmatory bifactor modelling is a factor analytic procedure that allows researchers to model unidimensionality and multidimensionality simultaneously. This method has important applications in the field of criminal psychology. Design/methodology/approach This paper begins by introducing the topic of factor analysis and explains how confirmatory bifactor modelling is similar yet distinct to the more familiar factor analytical procedures in the psychological literature. Findings Through practical examples this paper explains the value of this analytical technique to researchers in criminal psychology. Examples from the existing criminal psychological literature are used to illustrate the way in which bifactor analysis allows important theoretical questions to be addressed. Originality/value This paper highlights the strengths and limitations associated with traditional “restricted” confirmatory bifactor models and introduces the notion of the “unrestricted” bifactor model. The unrestricted bifactor model allows greater flexibility for addressing interesting research questions. The paper concludes by providing the reader with an annotated Mplus syntax file for how to perform confirmatory bifactor modelling.