Kreitman’s discussion of the Preventive Paradox in relation to the prevention of alcohol problems has had profound implications for alcohol policy and has generated considerable controversy. It is argued here that although Kreitman should be credited with the important observation that alcohol-related harm is not confined to a few dependent drinkers, nonetheless an apparent paradox is not an ideal platform from which to recommend policy. Furthermore, Kreitman's own data and data from an Australian survey of drinking are used to demonstrate that a commonplace truth underlies his apparently paradoxical findings. It is shown that the Preventive Paradox disappears when consideration is given to the amount of alcohol consumed on either (i) the day of highest alcohol intake out of the last four, or (ii) the day on which acute alcohol-related harm occurred. Episodic heavy consumption by persons whose average alcohol intake can be classified as ‘low’ or ‘medium’ risk contributes to the bulk of such experiences of harm. It is suggested that the importance of intoxication as a public health and safety issue has been neglected. This neglect is compounded when public education campaigns and prevention policy are only based on average rates of alcohol consumption. Advice regarding low risk levels of consumption for different types of harm should form one component of a comprehensive harm reduction policy. Other elements of such a policy should include a variety of other measures of proven effectiveness in relation to reducing levels of intoxication and related problems.