We investigate the optimal policy response to the possibility of abrupt, irreversible shifts in system dynamics. The welfare cost of a tipping point emerges from the policymaker's response to altered system dynamics. Our policymaker also learns about a threshold's location by observing the system's response in each period. Simulations with a recursive, numerical climate-economy model show that tipping possibilities raise the optimal carbon tax more strongly over time. The resulting policy paths ultimately lower optimal peak warming by up to 0.5°C. Different types of posttipping shifts in dynamics generate qualitatively different optimal pretipping policy paths.