Recent decades have seen the facilitation of unconventional or even extraordinary reproductive endeavours. Sperm has been harvested from dying or deceased men at the request of their wives; reproductive tissue has been surgically removed from children at the request of their parents; deceased adults’ frozen embryos have been claimed by their parents, in order to create grandchildren; wombs have been transplanted from mothers to their daughters. What is needed for requests to be honoured by healthcare staff is that they align with widely shared expectations about what people’s reproductive potential ought to be, what marital relationships ought to result in, and which kinds of ties are desirable between parents and children. Costly and invasive technologies are not considered excessive when they are used to support the building of appropriate families. However, deviations from dominant reproductive norms, even if technologically simple and convenient to the participants, are unlikely to receive support. In this paper, we offer examples of such deviations and explore their implications. If reproduction is important as a way of creating genetic relationships, should reproductive material in storage be offered to genetic relatives other than the people from whom it originated? And if parents are allowed to have reproductive material collected from their offspring, or even to use it to create babies, should offspring likewise be allowed to use their parents’ reproductive material? We tackle these questions and suggest ways in which interests in genetic ties could be operationalised in a more coherent and less-invasive manner than they currently are.