The contribution of heavy and moderate drinkers, respectively, to the rate of alcohol problems in society is evaluated for different types of risk functions. It is demonstrated that if the risk function is linear, the moderate drinkers will be responsible for the bulk of the problems. When the risk function is curved upwards, the heavy drinkers contribute a larger share of the problem. However, the risk function needs to be quite strongly curved before the majority of the problems can be attributed to the heavy drinkers. These calculations are based on certain empirically motivated assumptions about the distribution of the consumers along the consumption scale. The results suggest that the validity of the prevention paradox depends very much on the shape of the risk function, and hence that the role of the moderate drinkers may vary a lot across the spectrum of alcohol-related disabilities. For disabilities where the risk curve has a pronounced threshold-like form, the prevention paradox cannot be expected to apply. However, the role of the moderate drinker could be expected to be more significant for disabilities with a smoother and less convex risk curve. Accidents and social problems seem to fulfil the latter qualification, because the causal mechanism underlying such problems are connected to rates of acute intoxication, rather than to annual intake per se.