In this article, we summarise research that identifies best practice for communicating about hazards where the risk is low but public concern is high. We apply Peter Sandman's 'risk = hazard + outrage' formulation to these risks, and review factors associated with the amplification of risk signals. We discuss the structures that determine the success of risk communication strategies, such as the capacity for early communication to 'capture' the dominant representation of risk issues, the importance of communicating uncertainty, and the usefulness of engaging with communities. We argue that, when facing trade-offs in probable outcomes from communication, it is always best to choose strategies that maintain or build trust, even at the cost of initial overreactions. We discuss these features of successful risk communication in relation to a range of specific examples, particularly opposition to community water fluoridation, Ebola, and routine childhood immunisation.