Abstract. The COVID-19 pandemic confronts society with a dilemma between (in)visibility, security, and care. While invisibility might be sought by unregistered and undocumented people, being counted and thus visible during a pandemic is a precondition of existence and care. This article asks whether and how unregistered populations like undocumented migrants should be included in statistics and other “counting” exercises devised to track virus diffusion and its impact. In particular, the paper explores how such inclusion can be just, given that for unregistered people visibility is often associated with surveillance. It also reflects on how policymaking can act upon the relationship between data, visibility, and populations in pragmatic terms. Conversing with science and technology studies and critical data studies, the paper frames the dilemma between (in)visibility and care as an issue of sociotechnical nature and identifies four criteria linked to the sociotechnical characteristics of the data infrastructure enabling visibility. It surveys “counting” initiatives targeting unregistered and undocumented populations undertaken by European countries in the aftermath of the pandemic, and illustrates the medical, economic, and social consequences of invisibility. On the basis of our analysis, we outline four scenarios that articulate the visibility/invisibility binary in novel, nuanced terms, and identify in the “de facto inclusion” scenario the best option for both migrants and the surrounding communities. Finally, we offer policy recommendations to avoid surveillance and overreach and promote instead a more just “de facto” civil inclusion of undocumented populations.