Exposed disagreement is extremely rare in natural dialogue. Although informal argumentation features frequently in natural dialogue, the ways in which individuals make and evidence claims and position their opinions in relation to those of others is often achieved through more subtle and oblique methods. This makes natural dialogue distinct from more formal or institutionalised contexts. With increasing availability of natural dialogue datasets and with increasingly diverse contexts within which the application of argumentation modelling could be beneficial, being able to identify and interpret argumentation in natural dialogue becomes more important; so too does an understanding of why argumentation is enacted differently in natural dialogue and how factors such as politeness impact upon this. In this paper we highlight some of the ways in which argumentative content is produced differently in natural dialogue compared to formalised debate contexts and highly structured documents. We present some initial findings that demonstrate how existing models such as the Penn Discourse Treebank need further development if they are to adapt to the more dialogic data created on the social web.