This paper provides a first estimate of the potential greenhouse gas mitigation from the intra-sector reallocation of economic activity by the European manufacturing industry away from carbon-inefficient – or "brown zombie" – firms to more carbon-efficient firms. Using techniques from the literature on productivity, we find a potential reduction of 38% based on a limited reallocation of production, without the need for new technologies. Therefore, when designing emission reduction plans, policymakers should not focus solely on improvements and innovation within existing firms but must also encourage the reallocation of economic activity from "brown zombies" to more carbon-efficient enterprises.