Strict liability is widely seen as the most suitable way to govern highly risky activities, such as environmentally dangerous production or genetic engineering. The reason which is usually given for applying strict liability to these areas, is that not only efficient care is supposed to be induced but also an efficient level of the risky activity itself. It is argued that, in case of no market relationship between injurers and victims, this could only be achieved through strict liability but not via the negligence rule. In this paper we show that the superiority of strict liability does no longer persist in a world of risk averse parties. Our results suggest that in terms of risk allocation the negligence rule should be preferred for abnormally risky activities, if insurance markets are imperfect. The reason is that highly risky activities typically affect a large number of individuals, such that strict liability implies a quite unfavorable allocation of risk. Therefore the negligence rule turns out to be superior, if a market relationship between the parties exists, since it incurs less cost of risk. If there is no market relationship between injurer and victims, no clear result can be derived. The paper concludes with some remarks on the usefulness of upper bounds to an injurer's liability as well as regulations that exclude liability for unforeseeable losses. We argue that this kind of supplement to a strict liability rule can improve efficiency.