On the 5th of May 2020, a group of modellers, epidemiologists and biomedical scientists from the University of Edinburgh proposed a “segmenting and shielding” approach to easing the lockdown in the UK over the coming months. Their proposal, which has been submitted to the government and since been discussed in the media, offers what appears to be a pragmatic solution out of the current lockdown. The approach identifies segments of the population as at-risk groups and outlines ways in which these remain shielded, while ‘healthy’ segments would be allowed to return to some kind of normality, gradually, over several weeks. This proposal highlights how narrowly conceived scientific responses may result in unintended consequences and repeat harmful public health practices. As an interdisciplinary group of researchers from the humanities and social sciences at the University of Edinburgh, we respond to this proposal and highlight how ethics, history, medical sociology and anthropology - as well as disability studies and decolonial approaches - offer critical engagement with such responses, and call for more creative and inclusive responses to public health crises.