International climate negotiations take place in a setting where uncertainties regarding the impacts of climate change are very large. In this paper, we examine the influence of increasing the probability and impact of large climate change damages, also known as the 'fat tail', on the formation of an international mitigation agreement. We systematically vary the shape and location of the distribution of climate change damages using the stochastic version of the applied game-theoretical STACO model. Our aim is to identify how changes to the distributional form affect the stability of coalitions and their performance. We find that fatter upper tails increase the likelihood that more ambitious coalitions are stable as well as the performance of these stable coalitions. Fatter tails thus imply more successful, or 'fatter', international climate agreements.