The Paris Agreement calls for a cooperative response with the aim of limiting global warming to well below two degrees Celsius above pre-industrial levels while reaffirming the principles of equity and common, but differentiated responsibilities and capabilities(1). Although the goal is clear, the approach required to achieve it is not. Cap-and-trade policies using uniform carbon prices could produce cost-effective reductions of global carbon emissions, but tend to impose relatively high mitigation costs on developing and emerging economies. Huge international financial transfers are required to complement cap-and-trade to achieve equal sharing of effort, defined as an equal distribution of mitigation costs as a share of income(2,3), and therefore the cap-and-trade policy is often perceived as infringing on national sovereignty(2-7). Here we show that a strategy of international financial transfers guided by moderate deviations from uniform carbon pricing could achieve the goal without straining either the economies or sovereignty of nations. We use the integrated assessment model REMIND-MAgPIE to analyse alternative policies: financial transfers in uniform carbon pricing systems, differentiated carbon pricing in the absence of financial transfers, or a hybrid combining financial transfers and differentiated carbon prices. Under uniform carbon prices, a present value of international financial transfers of 4.4 trillion US dollars over the next 80 years to 2100 would be required to equalize effort. By contrast, achieving equal effort without financial transfers requires carbon prices in advanced countries to exceed those in developing countries by a factor of more than 100, leading to efficiency losses of 2.6 trillion US dollars. Hybrid solutions reveal a strongly nonlinear trade-off between cost efficiency and sovereignty: moderate deviations from uniform carbon prices strongly reduce financial transfers at relatively small efficiency losses and moderate financial transfers substantially reduce inefficiencies by narrowing the carbon price spread. We also identify risks and adverse consequences of carbon price differentiation due to market distortions that can undermine environmental sustainability targets(8,9). Quantifying the advantages and risks of carbon price differentiation provides insight into climate and sector-specific policy mixes.