Economists often regard broad-based carbon pricing (whether in the form of a carbon tax or cap and trade) as the most efficient policy to reduce carbon dioxide emissions. Relative to a narrower policy that exempts some emissions sources, a broader policy is often favored because it can exploit more low-cost emissions reduction opportunities and cause less emissions leakage to uncovered sources. Yet narrower approaches have gained considerable political support, partly because they avoid price increases for outputs (such as gasoline) regarded as especially critical to household budgets. Some analysts might lament any departure from broad carbon pricing, citing efficiency costs. This paper offers theory and numerical simulations revealing that such a shift need not sacrifice efficiency. This result reflects differences across sectors in distortions from preexisting taxes and in the elasticity of emissions with respect to the carbon price.