Though there is now growing commitment to publicly engaged research, the role and definition of the public in such processes is wide-ranging, contested and often rather vague. This article addresses this problem by showing that, although there is no single agreed upon theory or way of being public, it is still possible and very important to develop clear, public-centric, understandings of engaged research practice. The article introduces a multidimensional framework based on the theoretical literature on the 'public', and demonstrates – in the context of a recent engaged research project – how it is possible to conceptualize, design and evaluate context-specific formations of the public. Starting from an understanding of publics as mediated and dynamic entities, the article seeks to illuminate some of the choices that researchers face and how the framework can help them navigate these. This article is for all those interested in what it means to address, support and account for an engaged public in contemporary settings.