This paper provides a first analysis of optimal offset policies by a "policy bloc" of fossil fuel importers implementing a climate policy, facing a (non-policy) fringe of other importers, and a bloc of fuel exporters. The policy bloc uses either a carbon tax or a cap-and-trade scheme, jointly with a fully efficient offset mechanism for reducing emissions in the fringe. The policy bloc is then shown to prefer a tax over a cap-and-trade scheme, since 1) a tax extracts more rent as fuel exporters reduce the export price, and more so when the policy bloc is larger relative to the fringe
and 2) offsets are more favorable to the policy bloc under a tax than under a cap-and-trade scheme. The optimal offset price under a carbon tax is half the tax rate
under a cap-and-trade scheme the quota and offset price are equal. The domestic carbon and offset price are both higher under a tax than under a cap-and-trade scheme when the policy bloc is small
when it is larger the offset price can be higher under a cap-and-trade scheme. Fringe countries gain by mitigation in the policy bloc, and more under a carbon tax since the fuel import price is lower, and since the price obtained when selling offsets is often higher (always so for a large fringe).