The literature of welfare-maximising greenhouse gas emission reduction strategies pays remarkably little attention to equity. This paper introduces three ways to consider efficiency and equity simultaneously. The first method, inspired by Kant and Rawls, maximises net present welfare, without international co-operation, as if all regions share the fate of the region affected worst by climate change. Optimal emission abatement varies greatly depending on the spatial and temporal resolution, that is, the grid at which 'maximum impact' is defined. The second method is inspired by Varian's no-envy. Emissions are reduced so as to equalise total costs and benefits of climate change over the world and over time. Emission reductions are substantial. This method approximately preserves the inequities that would occur in a world without climate change. The third method uses non-linear aggregations of welfare (the utilitarian default is linear) in a co-operative setting. This method cannot distinguish between sources of inequity. The higher the aversion to inequity, the higher optimal greenhouse gas emission reduction.