Current climate policies are based on the use of Global Warming Potentials (GWPs) to compare emissions of various greenhouse gases. Yet, from an economic point of view, more efficient methods exist. We compare the potential costs of implementing some long-term goal for stabilization of the climate in three cases: Reduce CO2 emissions only, reduce emissions of the four greenhouse gases CO2, CH4, N2O and SF6 using the standard IPCC GWPs and reduce emissions of the same four gases with efficient and flexible, time dependent metrics. A multi-gas approach with GWPs reduces the costs by 8 percent when compared with CO2 reductions only, whereas the costs may be reduced by an additional 2 percent if using flexible metrics. If compared with the use of GWPs, we find that efficient weights increase the cost savings of including non-CO2 gases in climate policy by 15-40%, depending on the stabilization goal.