Lessons learnt from the exploration and understanding of agonistic dialogue assist the management of radical disagreement when conflict resolution fails. In these circumstances ‘dialogue for mutual understanding’ is premature. What is needed is the promotion of ‘dialogue for strategic engagement’, not less radical disagreement, but more. It is the strategic engagement of discourses (SED) – the logic of the war of words itself – that keeps open the possibility of future transformation when linguistic intractability closes down other forms of verbal communication. It clarifies what is at issue in the struggle between the challenging discourse, the hegemonic discourse, and the third-party (peacemaking) discourse, and what each of the competing discourses has to do in order to prevail. The distinction between extremism of ends and extremism of means is often a key to breaking the deadlock between undefeated conflict parties.