Ambidexterity research has proposed a variety of drivers to reconcile the partly conflicting forces of exploration and exploitation. However, little is known about how these drivers interact and whether they act as complements or substitutes. In a two-stage survey of small and medium-sized enterprises, we find that formal structural drivers and informal contextual drivers of ambidexterity do not demonstrate complementarity as is generally assumed, but rather act at cross-purposes with each other. Furthermore, we find that ambidextrous executives (those with high levels of behavioral complexity) appear to render the effects of the other two drivers relatively unimportant, and are only ever associated with moderate levels of ambidexterity. These findings permit the development of important theoretical insights for ambidexterity research and for the broader theory on organizational paradox.