Although emissions of CO2 are the largest anthropogenic contributor to the risks of climate change, other substances are important in the formulation of a cost-effective response. To provide improved facilities for addressing their role, we develop an approach for endogenizing control of these other greenhouse gases within a computable general equilibrium (CGE) model of the world economy. The calculation is consistent with underlying economic production theory. For parameterization it is able to draw on marginal abatement cost (MAC) functions for these gases based on detailed technological descriptions of control options. We apply the method to the gases identified in the Kyoto Protocol: methane (CH4), nitrous oxide (N2O), sulfur hexaflouride (SF6), the perflourocarbons (PFCs), and the hyrdoflourocarbons (HFCs). Complete and consistent estimates are provided of the costs of meeting greenhouse-gas reduction targets with a focus on "what" flexibility — i.e., the ability to abate the most cost-effective mix of gases in any period. We find that non-CO2 gases are a crucial component of a cost-effective policy. Because of their high Global Warming Potentials (GWPs) under current international agreements they would contribute a substantial share of early abatement.