The external accident cost of road use is a function of the marginal relationship between road use and accidents, as expressed, for instance, by the elasticity. This elasticity is, however, not necessarily constant, but may be assumed to depend on the traffic volume as seen in relation to road capacity. Dense or congested traffic may force speed levels down, decreasing the risk of accidents or at least the average loss incurred given that an accident takes place. Relying on a large econometric accident model based on monthly cross-section/time-series data for all provinces of Norway, we derive non-linear empirical functions describing the relationship between road use and accidents and discuss their implications in terms of accident costs and externalities. The analysis reveals that there is probably a large accident externality generated by heavy vehicle road use, but that the marginal external accident cost of private car use is quite small, perhaps even negative. To the extent that it is positive, it is so in large part on account of public and private insurance. Contrary to what is frequently believed and maintained, auto insurance does not serve to internalise the cost of accidents. In fact, its primary purpose and effect is exactly the opposite. The adverse incentives created by insurance could, however, be mitigated by certain innovative approaches to ratemaking. Such schemes would ideally involve more decision variables than just the decision to drive. Incentives could, in principle, be attached to speeding, route choice, vehicle choice, safety equipment, or time of day/week/year.