Effective Altruism (henceforth EA) is an influential new social movement and philosophical approach “which applies evidence and reason to working out the most effective ways to improve the world” and is dedicated to asking “How can I make the biggest difference I can?” (MacAskill 2016, Singer 2015) One of the core premises of EA is that the distribution of causes, charities, and interventions by effectiveness has a heavy tail. In other words, EA proponents claim that giving to the most effective charities produces "exponentially" more good than giving to charities that are moderately effective. We contend that EA should also attend to the other end of the distribution. For example, contributing to some projects can, intentionally or unintentionally, cause exponentially more harm than would otherwise occur in the status-quo. Identifying and preventing such projects should therefore also feature on the EA agenda. In this paper, we show that incorporating the other tail of the distribution has important implications for EA cause prioritization, for the methodology of EA meta-charities, and for the assessment of systemic as well as individual interventions. We also argue that the more complex picture of altruistic interventions that emerges from incorporating the other heavy tail suggests new EA responses to some prominent institutional critiques.