Numerous policy options exist to reduce future greenhouse gas emissions. A single-basket approach, which controls aggregate emissions, was adopted by the Kyoto Protocol. Such an approach allows emissions reductions of one gas to be traded with those of other gases in the “basket”, with the trade “price” determined by some weighting metric like the Global Warming Potential. To reduce stratospheric ozone depletion, the Montreal Protocol also dealt with controlling many compounds, but did so employing an alternative, multi-basket scheme. Trading was allowed within each basket, but not among baskets. While the Montreal Protocol has been highly successful using this approach, we show that if a single-basket approach had been adopted the short-term success could have been at risk due to the non-unique relationship between controls and environmental impacts when using a single basket. Using climate policy as an example, and without considering technological and economic constraints, we further show that the magnitude of the ambiguities in impacts associated with a single-basket approach depends on the rapidity of the emission phaseout. Fast phaseouts lead to less ambiguity than do slow ones. These results suggest that for each set of greenhouse gas control policies considered, the benefit of additional flexibility associated with a single-basket approach should be weighed against the associated increased uncertainties in the impacts to ascertain whether a single- or a multi-basket approach has the greater chance of successfully mitigating climate change.