Geoengineering technologies are by definition only effective at scale, and so international policy development of some sort will be unavoidable. It is therefore important to include this dimension when assessing the technologies’ feasibility and potential role in addressing climate change. The few existing studies that address this question indicate that policy development at the international level will be exceedingly difficult. This study provides an in-depth, theoretically informed analysis about why this might be the case. Using data in the form of negotiation proceedings, observations, and key-informant interviews with government officials from seven different countries, it argues that a significant part of the challenge lies in dissonances between problem definitions that characterize the geoengineering governance debate, and the structures and expectations that shape global environmental governance. These include a lack of institutional fit between the process-based differentiation of geoengineering technologies (CDR and SRM) and the international legal architecture; a lack of fit between the urgency of demanded governance action and prevalent scientific and political uncertainties; and a lack of fit between risk-risk trade-off narratives and the precautionary norms of environmental governance.