Conventional wisdom holds that the efficient way to limit warming to a chosen level is to price carbon emissions at a rate that increases exponentially. We show that this “Hotelling” tax on carbon emissions is actually inefficient. The least-cost policy path takes advantage of the climate system’s inertia by growing more slowly than exponentially. Carbon dioxide temporarily overshoots the steady-state level consistent with the temperature limit, and the efficient carbon tax follows an inverse-U-shaped path. Economic models that assume exponentially increasing carbon taxes are overestimating the minimum cost of limiting warming, overestimating the efficient near-term carbon tax, and overvaluing technologies that mature sooner.