Is there any number of people you should save from paralysis rather than saving one person from death? Is there any number of people you should save from a migraine rather than saving one person from death? Many people answer 'yes' and 'no', respectively. The aim of partially aggregative moral views is to capture and justify combinations of intuitions like these. These views contrast with fully aggregative moral views, which imply that the answer to both questions is 'yes', and with non-aggregative moral views, which imply that the answer to both questions is 'no'. In this article, I review the most natural and influential ways of developing partially aggregative views and explain the main problems they face. 1 | INTRODUCTION According to the moral view known as Act Utilitarianism, we should always maximize aggregate well-being. This view has plausible implications in a wide range of cases. However, it has very counterintuitive implications in cases in which we can save either a few people from severe burdens or many people from minor burdens. Suppose that in Death v Migraines: We can save either X from death or a huge number of people from migraines. Intuitively, we should save X, no matter how many people face migraines. But Act Utilitarianism implies that, if enough people face migraines, we should instead save them, for the well-being at stake for them will sum to more than the well-being at stake for X. There are other moral views that have this implication in Death v Migraines, and that have corresponding implications in equivalent cases. We can say that these views are fully aggregative. Act Utilitarianism is probably the most influential fully aggregative view, but these views can take many other forms. They can endorse moral options, which permit us to give extra weight to our own well-being and the well-being of those we love; require us to respect moral constraints, such as constraints against killing and breaking promises; and direct us to give extra weight to the well-being of the badly off. 1