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In the context of unequal deterministic longevities, classical utilitarianism exhibits, under time-additive individual preferences, a counterintuitive tendency to redistribute resources from short-lived agents towards long-lived agents, against any intuition for compensation. We examine the robustness of that result to the introduction of risky lifetime, and to a broader class of individual preferences. It is shown that classical utilitarianism remains unable to provide, in that broader framework, a general redistribution towards the short-lived. Then, we propose a remedy, which consists in imputing, when solving the social planner's allocation problem, the consumption equivalent of a long life to the consumption of long-lived agents. This compensation-constrained utilitarianism is shown to reduce welfare inequalities across agents with unequal lifetimes.