Contemporary biomedical research is conducted amidst regimes of national and transnational regulation. Regulation, like rules generally, cannot specify all the practicalities of their application. Regulations for biomedical research impose considerable constraints on laboratories and others. In principle, there is a never-ending regress whereby scientists have to provide increasingly more guarantees that protocols have been followed, standards reached and maintained, and rules adhered to. In practice, regulatory regress is not the actual outcome, as actors find ways of establishing closure for all practical purposes. Based on ethnographic case studies of two sites of biomedical work – the UK Stem Cell Bank and an anonymous laboratory working with primary human foetal material – this article documents the possibility of regulatory regress and strategies aimed at its closure.