Scientific expertise suggests that mitigating extreme world-wide climate change damages requires avoiding increases in the world mean temperature exceeding 2ê Celsius. To achieve the two degree target, the cumulated global emissions must not exceed some limit, the so-called global carbon budget. In a two-period twocountry general equilibrium model with a finite stock of fossil fuels we compare the cooperative cost-effective policy with the unilateral cost-effective policy of restricting emissions to the global carbon budget. In its simplest form, the cost-effective global policy is shown to consist of a joint emission trading scheme in the first period (only). In sharp contrast, subglobal cost-effective regulation may require the abating country to tax its first-period consumption and to tax or subsidize its emissions in the first and/or second period.