The construct of trait emotional intelligence (trait EI or trait emotional self-efficacy) provides a comprehensive operationalization of emotion-related self-perceptions and dispositions. In the first part of the present study (N=274, 92 males), we performed two joint factor analyses to determine the location of trait EI in Eysenckian and Big Five factor space. The results showed that trait EI is a compound personality construct located at the lower levels of the two taxonomies. In the second part of the study, we performed six two-step hierarchical regressions to investigate the incremental validity of trait EI in predicting, over and above the Giant Three and Big Five personality dimensions, six distinct criteria (life satisfaction, rumination, two adaptive and two maladaptive coping styles). Trait EI incrementally predicted four criteria over the Giant Three and five criteria over the Big Five. The discussion addresses common questions about the operationalization of emotional intelligence as a personality trait.