If a doctor is trying to decide whether or not to provide a medical treatment, does it matter ethically whether that treatment has already been started? Health professionals sometimes find it harder to stop a treatment (withdraw) than to refrain from starting the treatment (withhold). But does that feeling correspond to an ethical difference? In this article, we defend equivalence-the view that withholding and withdrawal of treatment are ethically equivalent when all other factors are equal. We argue that preference for withholding over withdrawal could represent a form of cognitive bias-withdrawal aversion. Nevertheless, we consider whether there could be circumstances in which there is a moral difference. We identify four examples of conditional nonequivalence. Finally, we reflect on the moral significance of diverging intuitions and the implications for policy. We propose a set of practical strategies for helping to reduce bias in end-of-life decision making, including the equivalence test.