Lexical cohesion not only contributes to the texture of a text, it can help to indicate the rhetorical development of the discourse. This article looks at this argument-structuring function of lexical cohesion first by considering single texts using the techniques of classical Discourse Analysis and then by using the methodology of corpus linguistics to examine several million words of text. First, the nature of cohesive links within single articles is examined. Next, the link between headlines and the articles that follow them is studied. Finally, various concessive mechanisms which structure arguments are examined in detail. It is argued that an awareness of the mechanisms outlined in this article will help students to understand better the kind of argumentation presented in texts. All the texts studied are from English newspapers.