We study international cooperation in a general environment with pecuniary and non-pecuniary externalities across countries. We derive two main theorems, each demonstrating that market-access commitments, a form of shallow integration, are sufficient to implement globally efficient policies. When all cross-border externalities are pecuniary, the first theorem provides a new and unifying perspective on a series of results by Bagwell and Staiger. When some cross-border externalities are non-pecuniary, the second theorem shows that market-access commitments, properly extended, still sustain global efficiency. These extended market-access commitments reinterpret cross-border externalities as additional goods that are traded and priced at their social values. We discuss the implications for international cooperation on climate change and geopolitics.