Suppose you perform two actions. The first imposes a risk of harm that, on its own, would be excessive; but the second reduces the risk of harm by a corresponding amount. By pairing the two actions together to form a set of actions that is risk-neutral, can you thereby make your overall course of conduct permissible? This question is theoretically interesting, because the answer is apparently: sometimes Yes, sometimes No. It is also practically important, because it bears on the moral (...) status of practices such as offsetting personal greenhouse gas (GHG) emissions. In this article we propose a criterion for distinguishing between cases where pairing risk-increasing and risk-reducing actions makes each action permissible, and those where it does not: the Principle of Aggregate Risk-Imposition. We work towards this by considering a range of examples that illustrate various illegitimate ways of pairing risk-increasing actions with risk-reducing ones, and asking what goes wrong in each case. We then use this criterion to evaluate GHG offsetting. Is offsetting a legitimate way of removing the risk-imposition associated with GHG emissions, or not? Controversially, we argue that this turns out to depend on the form that the offsetting takes. (shrink)