NEO instruments are widely used to assess Big Five personality factors, but confirmatory factor analyses (CFAs) conducted at the item level do not support their a priori structure due, in part, to the overly restrictive CFA assumptions. We demonstrate that exploratory structural equation modeling (ESEM), an integration of CFA and exploratory factor analysis (EFA), overcomes these problems with responses (N = 3,390) to the 60-item NEO-Five-Factor Inventory: (a) ESEM fits the data better and results in substantially more differentiated (less correlated) factors than does CFA; (b) tests of gender invariance with the 13-model ESEM taxonomy of full measurement invariance of factor loadings, factor variances-covariances, item uniquenesses, correlated uniquenesses, item intercepts, differential item functioning, and latent means show that women score higher on all NEO Big Five factors; (c) longitudinal analyses support measurement invariance over time and the maturity principle (decreases in Neuroticism and increases in Agreeableness, Openness, and Conscientiousness). Using ESEM, we addressed substantively important questions with broad applicability to personality research that could not be appropriately addressed with the traditional approaches of either EFA or CFA. (Contains 7 tables.)