Several countries have imposed either a ban or a tax on single-use plastic packaging, motivated by their contribution to marine plastic pollution. This may lead consumers to opt for similar unregulated substitutes, potentially undermining or even counteracting the intended effect of the policy instrument. The purpose of this study is to theoretically and empirically compare the environmental and welfare effects of the first-best Pigouvian taxes on both plastic bags and a substitute (paper bags), with two alternative second-best policy instruments: a tax on plastic products alone, and a common uniform tax on all packaging materials. The empirical analysis accounts for two different types of environmental externalities from the use of both bag types: marine pollution and greenhouse gas emissions. It also compares results for two countries, Denmark and the USA, which differ in the demand for plastic and paper bags. The theoretical analysis shows that a unilateral tax on plastic bags should equal the marginal environmental damage of plastic bags minus a fraction of the marginal environmental cost of paper bags, hence being lower than the Pigouvian tax. The optimal common tax should equal a weighted average of the marginal environmental damage of the two bag types and would be lower than the Pigouvian tax on plastics if the marginal external cost of plastic bags exceeds that for paper bags. The empirical analysis shows that for default parameters, the variation in tax level across the studied scenarios is small. It also shows that if Pigouvian taxes cannot be implemented, a common uniform tax on both bag types would result in a higher welfare gain than a tax on plastic bags alone. Sensitivity analysis reveals that the level of the second-best taxes and their associated environmental and welfare impacts are sensitive to assumptions regarding the littering rate and decay rate of plastic bags in the marine environment.