The Principle of Procreative Beneficence (PB) holds that when a couple plans to have a child, they have significant moral reason to select, of the possible children they could have, the child who is most likely to experience the greatest wellbeing – that is, the most advantaged child, the child with the best chance at the best life.1 PB captures the common sense intuitions of many about reproductive decisions. For example, many couples defer conceiving until they are in a better financial or social situation in an attempt to give their child a better life. Or a woman who is currently suffering from rubella may defer conception until she has recovered to prevent giving birth to a severely impaired child. In both of these cases, parents are choosing to have one child, who can expect a better life, over another, who could expect a worse life. Most people believe that such choices are morally permissible, if not morally required. PB extrapolates from our intuitions about such cases to cases involving selection using technological means, such as pre-implantation genetic diagnosis. PB does not posit an absolute moral obligation – it does not dictate what people must do. Instead it holds that there is a significant moral reason to select the best child, but one that must be weighed against other reasons. Many objections have been raised to PB. For example, it has been held that adopting the principle would exacerbate inequalities, since the wealthy would have better access to selection technologies than the poor;2 would reinforce objectionable societal preferences (such as preferences for children of a certain sex or sexual orientation);3 would impose unacceptable burdens on women4 and on parents in general;5 would result in a generation of disillusioned children, unable to achieve what is expected of them;6 and would generate an ‘arms-race’ as parents iteratively attempt to prevent their own children from being placed at a competitive disadvantage.7 The principle has also been criticised for failing to give parents all-things-considered guidance on what to do;8 failing to bridge the gap between what is best, and what parents think is best;9 ignoring the complexity and context-dependence of the good life;10 and being excessively individualistic.11 Savulescu and collaborators have responded to some of these objections elsewhere.12 In this paper we wish address a different and more practical objection: the objection that parents will be heavily restricted in the number of traits that they can select, since they will have to choose among a very limited number of embryos. Recent advances in stem cell research may provide a solution to this problem.