Despite the substantial literature on reported speech, its treatment in structural and quantitative-distributional analyses of discourse has remained problematic. This article surveys and discusses a range of methodological issues created by the occurrence of embedded segments of direct reported speech in narrative discourse. Analysis of a personal experience narrative from the Australian language Ganalbingu is used as illustration. Stories like this include substantial passages of direct reported speech. Detailed investigation of such stories allows us to address questions such as: (i) what is the narrative function of these passages of direct speech and (ii) how is reference to characters mapped across the distinct deictic frames represented by the narrated action and the represented speech of participants within the story world? It is argued that any approach to discourse structure which is formal or quantitative in orientation will need to address such issues. The article concludes by formulating some open questions for investigation which tease out cognitive predictions and assumptions implicit in the ways in which direct speech has previously been handled.