Recent ethical and legal challenges have arisen concerning the rights of individuals over their IVF embryos, leading to questions about how, when the wishes of parents regarding their embryos conflict, such situations ought to be resolved. A notion commonly invoked in relation to frozen embryo disputes is that of reproductive rights: a right to have (or not to have) children. This has sometimes been interpreted to mean a right to have, or not to have, one's own genetic children. But can such rights legitimately be asserted to give rise to claims over embryos? We examine the question of property in genetic material as applied to gametes and embryos, and whether rights over genetic information extend to grant control over IVF embryos. In particular we consider the purported right not to have one's own genetically related children from a property-based perspective. We argue that even if we concede that such (property) rights do exist, those rights become limited in scope and application upon engaging in reproduction. We want to show that once an IVF embryo is created for the purpose of reproduction, any right not to have genetically-related children that may be based in property rights over genetic information is ceded. There is thus no right to prevent one's IVF embryos from being brought to birth on the basis of a right to avoid having one's own genetic children. Although there may be reproductive rights over gametes and embryos, these are not grounded in genetic information.