Drawing upon multidimensional theories of intelligence, the current paper evaluates if the Geneva Emotional Competence Test (GECo) fits within a higher-order intelligence space and if emotional intelligence (EI) branches predict distinct criteria related to adjustment and motivation. Using a combination of classical and S-1 bifactor models, we find that (a) a first-order oblique and bifactor model provide excellent and comparably fitting representation of an EI structure with self-regulatory skills operating independent of general ability, (b) residualized EI abilities uniquely predict criteria over general cognitive ability as referenced by fluid intelligence, and (c) emotion recognition and regulation incrementally predict grade point average (GPA) and affective engagement in opposing directions, after controlling for fluid general ability and the Big Five personality traits. Results are qualified by psychometric analyses suggesting only emotion regulation has enough determinacy and reliable variance beyond a general ability factor to be treated as a manifest score in analyses and interpretation. Findings call for renewed, albeit tempered, research on EI as a multidimensional intelligence and highlight the need for refined assessment of emotional perception, understanding, and management to allow focused analyses of different EI abilities.