This paper tests Griceans' postulate for more minimal propositions for the role of what is said (conversational implicatures) against Contextualists' claim of a greater determination of what is said by contextual factors. It analyzes the predictions of three pragmatic processing models, embodying some of the assumptions of the rival views. The findings lend some initial support to a model in which both interpretations are constructed in parallel, with a bias towards the contextually enriched interpretations.