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Unilateral climate policy induces carbon leakage through the relocation of emission-intensive and trade-exposed industries to regions without emission regulation. Previous studies suggest that emission pricing combined with border carbon adjustment is a second-best instrument, and more cost-effective than output-based rebating. We show that the combination of output-based rebating and a consumption tax for emission-intensive and trade-exposed goods can be equivalent with border carbon adjustment. Moreover, it is welfare improving for a region that implements emission pricing along with output-based rebating to introduce such a consumption tax. The welfare gain is particularly large if output-based rebating is already implemented for a sector that is not much exposed to leakage, e.g., due to uncertainty about exposure or due to lobbying activities. Thus, supplementing output-based rebating with a consumption tax constitutes robust policies to mitigate carbon leakage.