The accumulation of pollution negatively impacts human health. Extreme increases in pollution, in particular, may have lethal implications for human beings, and, indeed, all living organisms. This paper thus devises a new model of economic growth that takes into account these lethal effects of accumulated pollution via a pollution threshold to show two key results. First, if an abatement technology is relatively inefficient, there exists a stationary steady state in which consumption and pollution stop growing. Second, if the abatement technology is sufficiently efficient, there exists a path along which pollution decreases at an accelerating rate until it finally reaches zero. In this case, consumption grows at a constant rate.