Abstract The implementation of climate policies in the US and EU in light of uncertainties about future international climate policy has shifted attention to two interrelated concerns, namely competitiveness and carbon leakage. Although various policy measures are available to address these concerns, there has been much discussion about one such measure in particular: the use of offsetting measures at the border. This article compares policy discussions in the US and the EU on how to address competitiveness and carbon leakage concerns, with a focus on the role of import-related border adjustment measures. It analyses the kinds of measures that so far have been put forward with a view to addressing competitiveness and carbon leakage; compares the approaches to the problems in the US and the EU; and provides a preliminary discussion of international cooperation on border adjustment measures. It concludes that two kinds of cooperation are needed between the EU and the US – not only cooperation through formal international negotiations, but also cooperation through international learning processes, in which the EU and the US learn from each other about design and implementation issues as they develop their respective cap-and-trade systems.