This paper uses the Theory of Enunciative Operations and suggests new concepts for a linguistic analysis of ‘pragmatic' effects such as the construction, through the use of grammatical markers, and connectives in particular, of indirect meaning, and argumentative force. Defining a three-term relation, the coordinator but is considered here as a counter-subordinator which both creates an argumentative domain attributed by the speaker to a previous utterance and corrects it in an interpersonal relation of discordance with the addressee. We propose a detailed contextualized analysis of the construction and retrieval of implicit utterances and argumentative power in interviews and political debates as the result of enunciative (versus extra-linguistic) operations marked by but interacting with a combination of specific markers within the utterances it links.