Atmospheric nuclear test detonations conducted by USA, USSR, UK, France and China, 1945–1980, generated radioactive particles that were dispersed by weather patterns, returning to earth as fallout. People who lived ‘downwind’ face ongoing risks from their exposure to ionizing radiation, as well as psychological, social, cultural and political distress. However, testing states obscured these humanitarian consequences by claiming that fallout could be contained to specific spatial zones, that there are ‘thresholds’ below which radiation exposure has negligible health impacts and that socio‐political forms of harm should be disregarded. While the scientific consensus concludes fallout circulates in complex, nonlinear patterns; there is no safe level of radiation exposure; and nuclear testing can generate tremendous anxiety, what Liboiron calls ‘threshold thinking’ continues to underlie policies ostensibly assisting victims of nuclear weapons. This article offers examples from responses to French Pacific nuclear testing, showing how access to compensation and other assistance has often been conditioned on threshold qualifications that function to limit downwind communities’ access to assistance and remedy. Victim assistance and environmental remediation obligations in the 2017 Treaty on the Prohibition of Nuclear Weapons offer opportunities to move beyond reductive policy logics to multifaceted, human rights‐based approaches to affected communities’ concerns.