Existing estimates of optimal climate policy ignore the possibility that carbon tax revenues could be used in a progressive way; model results therefore typically imply that near-term climate action comes at some cost to the poor. Using the Nested Inequalities Climate Economy (NICE) model, we show that an equal per capita refund of carbon tax revenues implies that achieving a 2 degrees C target can pay large and immediate dividends for improving well-being, reducing inequality and alleviating poverty. In an optimal policy calculation that weighs the benefits against the costs of mitigation, the recommended policy is characterized by aggressive near-term climate action followed by a slower climb towards full decarbonization; this pattern-which is driven by a carbon revenue Laffer curve-prevents runaway warming while also preserving tax revenues for redistribution. Accounting for these dynamics corrects a long-standing bias against strong immediate climate action in the optimal policy literature. Climate policy analyses often ignore the possibility of progressive redistribution of carbon tax revenues and assume that mitigation cost will burden the poor in the short term. Integrated Assessment Model (IAM) estimation suggests such redistribution could reduce inequality, alleviate poverty and increase well-being globally.