This study illustrates an overarching psychometric approach of broad relevance to investigations of 2 sources of construct-relevant psychometric multidimensionality present in many complex multidimensional instruments routinely used in psychological and educational research. These 2 sources of construct-relevant psychometric multidimensionality are related to (a) the fallible nature of indicators as perfect indicators of a single construct, and (b) the hierarchical nature of the constructs being assessed. The first source is identified by comparing confirmatory factor analytic (CFA) and exploratory structural equation modeling (ESEM) solutions. The second source is identified by comparing first-order, hierarchical, and bifactor measurement models. To provide an applied illustration of the substantive relevance of this framework, we first apply these models to a sample of German children (N = 1,957) who completed the Self-Description Questionnaire (SDQ–I). Then, in a second study using a simulated data set, we provide a more pedagogical illustration of the proposed framework and the broad range of possible applications of bifactor ESEM models.