This paper seeks to reopen the issue of whether Mrs Thatcher's interviews do show, as has been claimed, a distinctive pattern in that they are characterised by interviewers often gaining the floor through interruption at certain points in her speech because her turns appear to be complete at these points. Bull & Mayer (1988) have argued that earlier claims by Beattie (1982) and Beattie, Cutler & Pearson (1982) on this matter are suspect for a variety of methodological and statistical reasons. Each of their criticisms are addressed in this paper. It is argued that Bull & Mayer's study cannot be considered a direct test of the original hypothesis for a variety of reasons which are all outlined. The dialogue which is subsequently set up has implications far beyond the limited research question of the structure of Mrs Thatcher's political interviews and raises some compelling questions about the classification of all conversational turn-exchanges as well as the future development of schemes for classifying interruption.