One alleged weapon against unsustainable environmental impact is for the wealthy to consume less. This sufficiency strategy is to complement the efficiency strategy of lowering ratios of resource inputs to economic outputs; the former would reduce the affluence factor in I = PAT, the latter the technology factor. That the latter strategy suffers from a consumption rebound is widely recognized. This paper identifies a similar rebound when the affluence factor is autonomously lowered: The lower initial demand lowers prices, which in turn stimulates new demand by others. The strategy moreover addresses only the rich, raising questions of its theoretical maximum efficacy. Its proponents usually conflate frugality with the North–South dichotomy and intragenerational with intergenerational equity. Moreover, there are difficulties with the supporting arguments that frugality is good for one’s own sake as well as for the environment, and that the rich should ‘lead the way’ to living more lightly. Personal behaviour change is furthermore not a substitute for international political efforts. Finally, since all changes in right-side factors of the I = PAT equation change other right-side factors, such indirect attacks on impact should be abandoned in favor of supply and emissions quotas.