We derive non-cooperative Nash equilibrium (NE) importer and exporter petroleum excise taxes given full within-group tax coordination, but no coordination between groups, assuming that importers do not produce and exporters do not consume petroleum, and petroleum consumption causes a global externality. The aggregate NE tax is found to consist of an externality component and an optimal tariff component, and exceeds the standard Pigou tax. The environmental component in isolation is however less than the Pigou tax. With Stackelberg tax setting, the leader's tax is higher than in the Ne, and the follower's tax lower, and the overall tax higher. We show that importers prefer to set a tax instead of an import quota, since exporters' optimal response to a quota is a higher tax. An optimal cap-and-trade scheme will thus fare worse than an optimal tax scheme for importers, and will imply greater petroleum consumption and carbon emissions. When exporters behave as a cartel satisfying demand at a fixed export price, exporters' optimal tax is higher, while importers tax rule is Pigouvian. Exporters then gain at the expense of importers.