Meeting the net-zero climate target by 2050 has become a priority for the European Commission. The success of such objective largely depends on the design of COVID-19 economic recovery plans. In this paper we identify industrial sectors that, if governments are willing to decouple economic growth and emissions, should not benefit from recovery stimuli. Our results suggest that phasing-out the mining sector, a large provider of inputs to heavy polluting activities, would have large impacts on emissions once activity recovers. We also identify coke and refined petroleum products, chemical products and electricity and gas activities as critical downstream industries. Greening their output would limit GHG rebound effects in the coming months.