Can the structure of genetic and environmental influences on normative personality traits (NPTs), abnormal personality traits (APTs), and DSM-IV criteria for personality disorders (PD) fit a high or low congruence model positing, respectively, close or more limited etiologic continuity? Exploratory factor analysis was applied to transformed correlation matrices from Cholesky twin decompositions obtained in OpenMx. In 2801 adult twins from the Norwegian Institute of Public Health Twin Panel, NPTs and APTs were assessed by self-report using the Big Five Inventory (BFI) and PID-5-Norwegian Brief Form (PID-5-NBF), respectively. PDs were assessed at interview using the Structured Interview for DSM-IV Personality (SIDP-IV). The best model yielded three genetic and three unique environmental factors. Genetic factors were dominated, respectively, by (i) high loadings on nearly all PDs and NPT/APT neuroticism and compulsivity, (ii) negative loadings on NPT agreeableness/conscientiousness and positive loadings on APT/PD measures of antisocial traits, and (iii) negative loadings on NPT extraversion and histrionic PD, and positive loadings on APT detachment and schizoid/avoidant PD. Unique environmental factors were dominated, by (i) high loadings on all PDs, (ii) high loadings on all APT dimensions and NPT neuroticism, and (iii) negative loadings on NPT extraversion and positive loadings on NPT detachment/avoidant PD. Two genetic and one environmental common factor were consistent with a high congruence model while one genetic and two environmental factors were more supportive of a low congruence model. The relationship between genetic and environmental influences on personality assessed by NPTs, APTs, and PDs is complex and does not fit easily into a low or high congruence model.