Many who believe that human embryos have moral status are convinced that their use in human embryonic stem cell (hESC) research can be morally justified as long as they are discarded embryos left over from fertility treatments. This is one reason why this view about discarded embryos has played such a prominent role in the debate over publicly funding hESC research in the United States and other countries. Many believe that this view offers the best chance of a compromise between the different sides in this debate. This paper focuses on what seems to be the most plausible argument for this view about discarded embryos. It shows that this argument is unsound regardless of how one understands the claim that embryos have moral status. It also discusses the implications of this conclusion for attempts to use this argument as a basis for public policy.