As part of the European Green Deal, the EU is considering the introduction of a Border Carbon Adjustment (BCA) on imports as an alternative to free allocation of emission allowances to reduce the risk of carbon leakage under the EU’s Emissions Trading System (EU ETS). While a BCA for exports is not categorically excluded, it is less likely to be consistent with World Trade Organisation rules and therefore less likely to be proposed than an import-only BCA. In this paper, we show that replacing free allocation by an import-only BCA would weaken the competitiveness of EU producers in foreign markets. Free allocation also helps support the cost competitiveness of domestic products that are exported to non-EU markets. Therefore, a move to import-only BCAs does not necessarily make redundant the continued use of free allocation to help safeguard overall industrial competitiveness. While combining an import BCA with free allocation for exports can increase the risk of legal challenges, such risks may be reduced with an appropriate design. More broadly, policymakers need to navigate a complex trade-off between competitiveness support, a stronger carbon price signal, and extra fiscal revenue.