Many people think that, faced with a choice between saving a life and averting a headache, one must save the life no matter how many people one could otherwise spare from suffering a headache. One can justify this intuition in different ways. In this paper, I consider the idea that the underlying problem is with a certain kind of aggregation, and ask how to apply that kind of anti-aggregationism to decision-making under risk. After all, nobody thinks that one must prioritise any probability (however small) of saving a life, when balanced against any number of people whose headaches one can surely avert. Here are the desiderata (expressed in terms of harms, for simplicity, but they could be generalised):

1. When the risked harms are of the same order, minimise expected harm.
2. When the risked harms are of a different order, and the probability of the more serious harm is high enough, prioritise the more serious harm at any cost with respect to the lesser harm.
3. When the risked harms are of a different order, and the probability of the more serious harm is low enough, minimise expected harm.
4. When facing a series of choices to spare people from a minor harm, each of which imposes a very low risk of a more serious harm, but where the series has a very high risk of the more serious harm, minimise expected harm.

In the longer version of the paper, I show how no straightforward decision-theoretic approach to anti-aggregation can accommodate these desiderata. But in this presentation—after briefly motivating an anti-aggregationist moral theory—I will concentrate on introducing my own principle that does satisfy them.