We analyze how N firms producing a commodity good with a polluting by-product respond to environmental taxes. These firms vary in operational and environmental efficiency. Under Cournot competition, we examine two demand functions: iso-elastic and linear. We establish the existence and uniqueness of the equilibrium and how it changes with tax levels and environmental efficiency. Our findings suggest that taxes may not always benefit firms with green, low-cost technologies, as they erode the advantages of operational efficiency. Additionally, total and per-unit emissions may increase with higher taxes or improved environmental efficiency. Finally, the observed effects can qualitatively differ based on the form of market demand.