Internalizing the global negative externality of carbon emissions requires flattening the extraction path of world fossil energy resources (= world carbon emissions). We consider governments having sign-unconstrained emission taxes at their disposal and seeking to prevent world emissions from exceeding some binding aggregate emission ceiling in the medium term. Such a ceiling policy can be carried out either in full cooperation of all (major) carbon emitting countries or by a sub-global climate coalition. Unilateral action has to cope with carbon leakage and high costs which makes a strong case for choosing a policy that implements the ceiling in a cost-effective way. In a two-country two-period general equilibrium model with a non-renewable fossil-energy resource we characterize the unilateral cost-effective ceiling policy and compare it with its fully cooperative counterpart. We show that with full cooperation there exists a cost-effective ceiling policy in which only first-period emissions are taxed at a rate that is uniform across countries. In contrast, the cost-effective ceiling policy of a sub-global climate coalition is characterized by emission regulation in both periods. That policy may consist either of positive tax rates in both periods or of negative tax rates (= subsidies) in both periods or of a positive rate in the first and a negative rate in the second period. The share of the total stock of energy resources owned by the sub-global climate coalition turns out to be a decisive determinant of the sign and magnitude of unilateral cost-effective taxes.