We examine the lifetime incidence and intergenerational distributional effects of an economywide carbon tax swap using a numerical dynamic general equilibrium model with overlapping generations of the U.S. economy. We highlight various fundamental choices in policy design including (1) the level of the initial carbon tax, (2) the growth rate of the carbon tax trajectory of over time, and (3) alternative ways for revenue recycling. Without revenue recycling, we find that generations born before the tax is introduced experience smaller welfare losses, or even gain, relative to future generations. For sufficiently low growth rates of the tax trajectory, the impacts for distant future generations decrease over time. For future generations born after the introduction of the tax, the negative welfare impacts are the smallest (largest) when revenues are recycled through lowering pre-existing capital income taxes (through per-capita lump-sum rebates). For generations born before the tax is introduced, we find that lump-sum rebates favor very old generations and labor (capital) income tax recycling favors very young generations (generations of intermediate age).