We propose a simple model of civil conflict between a moderate faction and two extremist factions of “hardliners”. Hardliners strongly dislike any position that dif- fers from their ideological position, but barely distinguish between positions closer and farther from it. For a pre-determined set of ideological positions, each faction chooses whether to exert effort to coerce other factions. Full-scale conflict arises whenever two or more factions exert effort. We show that there exist circumstances under which more radical extremist positions ultimately induce moderate and pe- aceful outcomes. We discuss how a third party can therefore induce moderate and peaceful outcomes by means of favoring more radical leaderships in extremist facti- ons. Such an intervention can be successful only if the cost of fighting is sufficiently large. Otherwise, it induces more conflict and more radical outcomes. Interventions that reduce the cost of conflict increase both the likelihood of full-scale conflict and radical outcomes.