The Paris Agreement, which entered into force in 2016, sets the ambitious climate change mitigation goal of limiting the global temperature increase to below 2°C and ideally 1.5°C. This puts a severe constraint on the remaining global GHG emissions budget. While international shipping is also a contributor to anthropogenic GHG emissions, and CO2 in particular, it is not included in the Paris Agreement. This article discusses how a share of a global CO2 budget over the twenty-first century could be apportioned to international shipping, and, using a range of future trade scenarios, explores the requisite cuts to the CO2 intensity of shipping. The results demonstrate that, under a wide range of assumptions, existing short-term levers of efficiency must be urgently exploited to achieve mitigation commensurate with that required from the rest of the economy, with virtually full decarbonization of international shipping required as early as before mid-century.