To limit the probable increase in global mean temperature to 2 °C, about 80%, 50% and 30% of existing coal, gas and oil reserves, respectively, would need to remain under the soil. While the concept of ‘unburnable fuels’ has become prominent, there has been little discussion on institutional mechanisms to identify specific fossil fuel reserves to be left untouched and the financial mechanisms for raising and distributing funds to compensate the right-holders for forgoing extraction. We present an auction mechanism to determine the fossil fuel reserves to be kept untapped – those whose extraction would generate the least rents, ensuring cost efficiency. The auctions could be complemented by other provisions to reap collateral benefits of avoided extraction, for example by prioritizing reserves that coincide with outstanding socio-environmental values that are likely to be disrupted by the extraction of fossil fuels. We also discuss how to raise funds, for example through a fossil fuel producers-based tax, to finance the mechanism compensating right-holders and ensuring commitment. The effective identification of unburnable fossil fuel reserves and the development of accompanying funding mechanisms seems to be the elephant in the room of climate negotiations and we aim at contributing to an overdue discussion on supply-side interventions to mitigate greenhouse gas emissions.