Conversation Analysis (CA) and Discursive Psychology (DP) reject the view that assumptions about cognitive processes should be used to account for discursive phenomena. Instead, cognitive issues are respecified as discursive phenomena. Discursive psychologists do this by studying discursive practices of talking about mental phenomena and using mental predicates. This approach is exemplified by a study of the use of constructions with German "verstehen" ("to understand") in conversation. Some conversation analysts take another approach, namely, inquiring into how participants display mental states in talk-in-interaction. This is exemplified by a study of how grammatical constructions are used to display different types of inferences drawn from a partner's prior turn. It will be argued that the constructivist, anti-essentialist stance which CA and DP take with regard to cognition is a prosperous line of research, which has much in its favor from a methodological point of view. However, it can be shown that tacit assumptions about cognitive processes are still inevitable when doing CA and DP. As a conclusion, the paper pleads for an enhanced awareness of how cognitive processes come into play when analysing talk-in-interaction and it advocates the integration of a more explicit cognitive perspective into research on talk-in-interaction.