This paper introduces the Monstrous Conclusion, according to which, for any population, there is a better population consisting of just one individual (the Monster). The Monstrous Conclusion is deeply counterintuitive. I defend a version of Prioritarianism as a particularly promising population axiology that does not imply the Monstrous Conclusion. According to this version of Prioritarianism, which I call Asymptotic Prioritarianism, there is diminishing marginal moral importance of individual welfare that can get close to, but never quite reach, some upper limit. (...) I argue that Asymptotic Prioritarianism faces a theoretical cost, that I call the Absolute Priority Principle. However, the Absolute Priority Principle is an extreme version of what I call the Trade-off Condition, an already noteworthy problem facing other (more widely endorsed) versions of Prioritarianism. I conclude that it is better for a theory to imply the Absolute Priority Principle and avoid the Monstrous Conclusion than to imply the Monstrous Conclusion and the Trade-off Condition. The potential for Asymptotic Prioritarianism is substantial. (shrink)