For a policy-maker promoting the end of a harmful tradition, conformist social influence is a compelling mechanism. If an intervention convinces enough people to abandon the tradition, this can spill over and induce others to follow. A key objective is thus to activate such spillovers and amplify an intervention's effects. With female genital cutting as a motivating example, we develop empirically informed analytical and simulation models to examine this idea. Even if conformity pervades decision-making, spillovers can range from irrelevant to indispensable. Our analysis highlights three considerations. First, ordinary forms of individual heterogeneity can severely limit spillovers, and understanding the heterogeneity in a population is essential. Second, although interventions often target samples of the population biased towards ending the harmful tradition, targeting a representative sample is a more robust way to achieve spillovers. Finally, if the harmful tradition contributes to group identity, the success of spillovers can depend critically on disrupting the link between identity and tradition.