This paper extends previous work which provided a theory for the interpretation of and necessity for clue words in a particular kind of discourse - namely, one-way arguments. Previous work described a taxonomy of connective clues (words such as "hence" or phrases such as "as a result"), where each clue, classified according to the taxonomy, would set in place a default interpretation of its containing proposition, with respect to the representation for the argument so far. In this paper, we examine how to combine the restrictions for clues with a basic processor for the discourse, offering a integrated processing algorithm, which takes advantage of clues to reduce processing and to detect incoherent arguments, and can still produce an analysis in the absence of clues. We conclude with some suggestions for incorporating clues of re-direction and clues that signal exceptional transmissions. We also demonstrate the implications of our results for discourse in general.