Signalling one of the new directions now emerging alongside (Critical) Discourse Analysis, Jim Martin and David Rose (2003) have called for more Positive Discourse Analysis. PDA describes what texts 'do well' and 'get right' in our eyes. This paper thus investigates strategies for propelling marginal discourses into the mainstream news media. News stories tend to appear in the press within overarching 'frames' (Gamson 1989; Lakoff 2002), e.g. in an analysis of 1,000 news items on the Russian-Chechen conflict, the 'Villain-Victim' frame is widespread (to caricature: Russians are human-rights-abusing aggressors; Chechens are oppressed independence-fighters). Interviews with journalists support this textual analysis. Only very rarely do news stories successfully contest the dominant frames. The paper (i) discusses current research on counter-discourse, (ii) takes a case study approach to illustrate five strategies used in those few texts which contest the mainstream discourse, and (iii) suggests more general explanations - drawn from lexicogrammatical analysis, media practices, cognitive linguistics and psychology - as to why the 'radical reframing' strategy works. Despite the small scale nature of this analysis, it illuminates a useful application of PDA. Identifying which reframings resonate with editors (i.e. are selected for publication) could guide academics wishing to publicly contest media coverage of their areas of expertise or other socially salient issues.