We evaluate the joint use of satellite-observed intensity of urban nightlights and census-based population density data as constraints on the spatial structure of CO2 emissions from fossil fuels. Findings are: (1) the probability that population density exceeds a given value follows a power-law distribution over two orders of magnitude of population density, encompassing the 40% of the global population at the highest densities. (2) The corresponding probability distribution for nightlights intensity also follows a power-law, departing near instrumental saturation. (3) Assuming that the true nightlights intensity distribution follows the power-law above instrumental saturation, we obtain a correction for saturation errors in the nightlights data. The amplification of nightlights intensity required to correct for saturation errors is estimated to be a factor of 1.15–1.23 globally and much greater in regions with high nightlights intensities. (4) Correcting for saturation, we observe clear empirical relationships between nightlights intensity and areal densities of energy consumption, fossil-fuel emissions and economic activity, holding throughout the development spectrum. (5) We indicate how these relationships underpin a fossil-fuel data assimilation system (FFDAS) for estimating fossil-fuel CO2 emissions.