This paper examines the linking of price-based and quantity-based provision of a public good by two parties in the example of pollution control under a global quantity constraint, using a stochastic partial-equilibrium model. One country chooses a price-based instrument (tax) and trades with another that lets its emissions price adjust. The expected cost for the price-setting country and the combined expected cost is higher than if both countries choose a quantity-based instrument, and the country with the quantity instrument stands to benefit in terms of expected net costs. The effect increases when the relative size of the country with the price-based constraint increases; and increases with respect to the degree of correlation in ex-ante uncertain abatement costs. While the quantity-setting country benefits from lower expected costs in most circumstances, the variance in cost can be much higher if its costs are correlated with the price-setting country. The optimal ex-ante tax rate differs from that under quantity-quantity linking. These results have important implications for instrument choice for the regulation of greenhouse gases and other pollutants and for the design of international agreements when there are domestic preferences for price