This article presents a dual‐process model of media entertainment representing 2 psychological appraisal processes, and examines how these processes evoke appreciation or enjoyment as a function of the presence/absence of cognitive conflict. The first process (which characterizes experiences of appreciation) is deliberative and slow, and results from cognitive conflict. The second process (which characterizes experiences of enjoyment) is automatic and fast, and occurs when cognitive conflict is inconsequential. Both appraisal processes result from the same underlying framework of intuitive preferences. 2 studies vary narrative conflict among sets of intuitive moral domains to test dual‐process predictions regarding slow/fast response times and the association of the presence/absence of conflict with self‐reported experiences of appreciation/enjoyment. Discussion examines theoretical implications for entertainment research.