The paper aims to clarify the Relevance theoretic notion of procedural meaning (cf. Blakemore 1987, Wilson & Sperber 1993) through the analysis of but and nevertheless. I show, first, that a procedural analysis is able to account for differences between these expressions that cannot be explained in terms of the speech-act theoretic notion of non-truth conditional indicators, and, second, that these differences show that the conception of procedural meaning as a constraint on contextual effects (cf. Blakemore 1987) is too narrow and must be extended to include all information about the inferential processes involved in utterance interpretation, including context selection.