The present study sought to (1) determine whether Barrett's counterintuitiveness coding and quantifying scheme (CI-Scheme) could be applied to cultural materials with sufficient intercoder reliability, (2) provide evidence concerning just how counterintuitive is too counterintuitive for a concept to be a recurrent cultural idea, and (3) test whether counterintuitive intentional agent concepts are more common in folktales than other classes of counterintuitive concepts. Seventy-three folktales from around the world were sampled from larger collections. Using Barrett's CI-Scheme, two independent coders identified 116 counterintuitive objects and scored them for degree of counterintuitiveness with very high inter-rater concordance. Of folktales, 79% had one or two counterintuitive objects. Of the counterintuitive objects 93% had a counterintuitiveness score of only one. Of counterintuitive objects, 98% were agents. Results suggest the CI-Scheme may have utility for analyzing cultural materials, that the cognitive optimum for cultural transmission falls around one counterintuitive feature, and that counterintuitive agents are more common than other types of counterintuitive objects in folktales.