For decades, the object of international climate governance has been greenhouse gases. The inadequacy of decarbonization based on this system has prompted calls to expand climate governance to include restrictions on fossil fuel supply. Such initiatives could rely on accountability frameworks based on fossil fuel reserves, production, or infrastructure, yet there has been little consideration of the different implications of these options. We inform such discussions by undertaking a sociotechnical analysis of existing schemes for the monitoring, reporting and verification of fossil fuels. We identify serious risks from anchoring climate governance in fossil fuel reserves. More promising directions for supply-side governance lie in accountability frameworks based on a combination of fossil fuel production volumes and infrastructure, since these are more transparent to multiple actors. This transparency would provide much-needed opportunities for democratic oversight of the data underpinning climate governance, opening new channels for holding states accountable for their climate performance.