International carbon markets can be an important tool in achieving countries’ mitigation targets under the Paris Agreement, but they are subject to a number of environmental integrity risks. An important risk is that some countries have mitigation targets that correspond to higher levels of emissions than independent projections of their likely emissions. If such ‘hot air’ can be transferred to other countries, it could increase aggregated emissions and create a perverse incentive for countries not to enhance the ambition of future mitigation targets. Limits to international transfers of mitigation outcomes have been proposed to address this risk. This article proposes a typology for such limits, explores key design options, and tests different types of limits in the context of 15 countries. Our analysis indicates that limits to international transfers could, if designed appropriately, prevent most of the hot air contained in current mitigation targets from being transferred, but also involve trade-offs between different policy objectives. Given the risks from international transfer of hot air and the uncertainty over whether other approaches will be effective in ensuring environmental integrity, we recommend that countries take a cautious approach and pursue a portfolio of approaches to ensure environmental integrity, in which case limits could provide for additional safeguards. Key policy insights Limits to international transfers involve trade-offs between different policy objectives, in particular reducing the risk that countries transfer hot air and enabling participation in carbon markets. Under ‘relative’ limits a country may transfer mitigation outcomes to the extent that its actual emissions are below the limit. Relative limits derived from historical emissions data have significant limitations, and none of the tested approaches was found to be effective for all countries. Relative limits based on emission projections could be a more valid approach, although they are also technically and politically challenging. Under ‘absolute’ limits a country could only issue, transfer or acquire a certain amount of mitigation outcomes. Absolute limits set at sufficiently low levels could prevent countries from transferring large amounts of hot air, but are bluntly applicable to all countries, whether or not they have hot air.