Recent studies suggest that counterintuitive ideas embedded in stories facilitate their subsequent recall, thus increasing the likelihood that such stories survive time and space. However, it could be that structure of counterintuitive stories affects memory rather than the distinctiveness of their contents. Indeed, Harmon-Vukic and Slone (2009) demonstrated that integration of story information eliminated the counterintuitiveness effect. The purpose of the present experiment was to further explore the influence of integration on memory for counterintuitive concepts. Participants were presented with a story containing elements that were either intuitive, minimally counterintuitive, or maximally counterintuitive. In addition, the stories were either integrated or not integrated. Participants were asked to recall the material either immediately, or one week later. Consistent with the results of Harmon-Vukic and Slone recall performance was best for integrated stories, regardless of level of intuitiveness. The same effect occurred on week later, although overall memory performance was lower.