The asymmetry is the view in population ethics that, while we ought to avoid creating additional bad lives, there is no requirement to create additional good ones. The question is how to embed this intuitively compelling view in a more complete normative theory, and in particular one that treats uncertainty in a plausible way. While arguing against existing approaches, I present new and general principles for thinking about welfarist choice under uncertainty. Together, these reduce arbitrary choices to uncertainty-free ones, regardless (...) of how the latter should be made. I illustrate these principles by developing two theories of the asymmetry, reflecting different views about the non-identity problem. In doing so, I clarify some other major choice-points, presenting new arguments that creating additional good lives can justify (but not require) doing harm. Finally, I consider what the developed theories have to say about the importance of extinction risk and the long-run future. (shrink)