A number of proposals have been put forth regarding the proper way to model the societal impact of fatal accidents. Most of these proposals are based on some form of utility function asserting that the social cost (or disutility) of N lives lost in a single accident is a function of Nα. A common view is that a single large accident is more serious than many small accidents producing the same number of fatalities, hence α > 1. Drawing upon a number of empirical studies, we argue that there is insufficient justification for using any function of N fatalities to model societal impacts. The inadequacy of such models is attributed, in part, to the fact that accidents are signals of future trouble. The societal impact of an accident is determined to an important degree by what it signifies or portends. An accident that causes little direct harm may have immense consequences if it increases the judged probability and seriousness of future accidents. We propose that models based solely on functions of N be abandoned in favor of models that elaborate in detail the significant events and consequences likely to result from an accident.