Genetic and environmental sources of covariation among cognitive measures of verbal IQ, performance IQ (PIQ), academic achievement, 2-choice reaction time (CRT), inspection time (IT) and the 6 Openness facets of the NEO Personality Inventory-Revised (NEO PI-R) were examined. The number of twin and twin-sibling pairs ranged from 432 (182 MZ, 350 DZ/sibling) to 1023 (273 MZ, 750 DZ/sibling) for cognitive measures, and between 432 (90 MZ, 342 DZ/sibling) - 437 (91 MZ, 346 DZ/sibling) for Openness facets. Structural equation modeling best supported a model with a 3-factor additive genetic structure. A genetic general factor subsumed the 5 cognitive measures and 5 of the 6 Openness facets (Actions did not load significantly). A second additive genetic factor incorporated the 6 Openness facets, and a third additive genetic factor incorporated the 5 cognitive measures. Specific additive and dominance genetic effects were also evident, as were shared common and shared unique environmental influences, and specific unique environmental effects. The Openness facets of Ideas and Values evidenced the strongest phenotypic correlations with cognitive indices, particularly verbal measures. The genetic correlations among Openness facets and cognitive measures ranged from -.06 to .79. Results were interpreted as suggesting that Openness is related to general cognitive ability (g) through a genetic mechanism and that gengenders a minor but discernable disposition towards Openness for the majority of facets.