To date, no studies have examined a range of structural models of the interpersonally aversive traits tapped by the Short Dark Tetrad (SD4; narcissism, Machiavellianism, psychopathy, sadism), in conjunction with their measurement invariance (males vs. females) and how the models each predict external correlates. Using a large sample of young adults (N = 3,975), four latent variable models were compared in terms of fit, measurement invariance, and prediction of intrapersonal and interpersonal functioning. The models tested were as follows: (Model A) confirmatory factor analytic, (Model B) bifactor, (Model C) exploratory structural equation model, and (Model D) a reduced-item confirmatory factor analytic that maximized item information. All models accounted for item covariance with good precision, although differed in incremental fit. Strong invariance held for all models, and each accounted similarly for the external correlates, highlighting differential predictive effects of the SD4 factors. The results provide support for four theoretically distinct but overlapping dark personality domains.