Both intuition and rationality can play important roles in strategic decision making. However, a framework that specifically accounts for the interplay between intuition and rationality is still missing. This study addresses this gap by using a paradox lens and conceptualizes the intuition–rationality duality as a paradoxical tension. We draw on seven case studies of innovation projects to empirically derive a three-step process for managing this intuition–rationality tension through paradoxical thinking. Our empirical data suggest that management of the tension starts with preparing the ground for paradoxical thinking by creating managerial acceptance for the contradictory elements of rational and intuitive approaches to decision making. The process then continues by developing decision-making outcomes through the integration of intuitive and rational practices. Finally, the outcomes of paradoxical thinking are embedded into the organizational context. For each step of the model, we indicate a set of practices that, by leveraging intuitive or rational characteristics of decision making, practitioners can use to deal with this cognitive tension in the different steps of our model.