We combine theoretical and numerical analysis to derive optimal combinations of output-based allocation of emissions allowances and consumption taxes, where ‘optimal’ means from a global or regional welfare perspective. A key analytical finding is that output-based allocation of emissions allowances and consumption taxes are complements rather than substitutes. A key numerical finding is that the optimal output-based allocation and consumption tax should be set at almost the same rate relative to the emissions intensity times the emissions price, and increase substantially with the stringency of the emissions reduction targets. Also, inclusion of Scope 2 emissions is crucial for the optimal policy combination.