Rate-based emissions policies (like tradable performance standards) fix average emissions intensity, while cap-and-trade policies fix total emissions. This paper shows that unfettered trade between rate-based and cap-and-trade programs always raises combined emissions, except when product markets are related in particular ways. Gains from trade are fully passed on to consumers in the rate-based sector, resulting in more output and greater emissions allocations. We consider a range of policy options to offset the expansion, including unilateral ones when jurisdictional differences require. The cap-and-trade jurisdiction could impose an "exchange rate" to adjust for relative permit values, but marginal abatement cost equalization is sacrificed. Still, that jurisdiction may prefer adjusted trade over tightening their own cap, which transfers away rents. Although the rate-based sector would have to implement the switch to output-based allocation of a cap, its surplus would be higher than with adjusted trade, which is also preferred to no trade. The cap-and-trade sector would also be better off. Thus, a range of combinations of tighter allocations could improve situations in both sectors with trade, while holding emissions constant.