Much philosophical attention has been paid to the question of whether, and why, one may divert a runaway trolley away from where it will kill five people to where it will kill one. But little attention has been paid to whether the reasons that ground a permission to divert thereby ground a duty to divert. This paper defends the Requirement Thesis, which holds that one is, ordinarily, required to act on lesser-evil justifications for harming for the sake of others. Cases in which we have lesser-evil justifications of harming for the sake of others are rescue cases. Ordinarily, an agent is under a duty to rescue unless doing so imposes too great a cost on her, or violates someone else's rights. When neither of these defeating conditions obtain, one is required to rescue even if this involves causing harm to innocent people.