In a widely cited paper, Andreoni and Levinson (2001) argue that, under very mild restrictions on preferences, increasing returns to scale in pollution abatement are a sufficient condition for pollution to ultimately fall to zero with income growth. We show that the existence of an Environmental Kuznets Curve depends on the relative magnitudes of the returns to scale in abatement and in gross pollution, rather than on their absolute values. Increasing returns to scale in abatement by themselves are not sufficient for pollution to fall with income unless the returns to scale of abatement exceed the returns to the production of gross pollution.