We assess five proposals for the future of the EU greenhouse gas Emission Trading Scheme (ETS): pure grandfathering allocation of emission allowances (GF), output-based allocation (OB), auctioning (AU), auctioning with border adjustments (AU-BA), and finally output-based allocation in sectors exposed to international competition combined with auctioning in electricity generation (OB-AU). We look at the impact on production, trade, CO2 leakage and welfare. We use a partial equilibrium model of the EU 27 featuring three sectors covered by the EU ETS – cement, steel and electricity – plus the aluminium sector, which is indirectly impacted through a rise in electricity price. The leakage ratio, i.e. the increase in emissions abroad over the decrease in EU emissions, ranges from around 8% under GF and AU to -2% under AU-BA and varies greatly among sectors. Concerning the overall economic cost, OB appears to be the least efficient policy, even when taking into account its ability to prevent CO2 leakage. On the other hand, this policy minimises production losses and wealth transfers among stakeholders, which is likely to soften oppositions. GF and AU are the most efficient policies from an EU perspective, even when leakage is accounted for. From a world welfare perspective and whatever the emission reduction, AU-BA is the least costly policy, while OB-AU, AU and GF entail similar costs.