Road safety is a major concern in the West, especially in France. Among all the established risk factors for fatal crashes, speed is specific in two ways: every road-user is exposed to it, and it increases not only crash rates but also the severity of crashes. Thus, speed regulation is of primary importance in road-safety policy and has also generated much public debate. To contribute to this debate, we constructed a power-model which relates the number of fatal crashes to speed raised to the power four. Despite its simplicity, this model fitted the data well. Notably, it enabled the fractions of fatal crashes attributable to various levels of speeding to be estimated. Data for secondary roads over the period 2001–2010 showed that the fraction of fatal crashes attributable to high-level speeding (>20 kph over the speed limit) decreased from 25% to 6% and that attributable to medium-level speeding (10–20 kph over the speed limit) decreased from 13% to 9%, whereas that attributable to low-level speeding progressively increased from 7% to 13%. Similar trends were observed on main roads. These results highlight the effectiveness of the speed regulation policies introduced during the study period with respect to high-level speeding. They also suggest that future policy should focus on low and medium-level speeding in order further to reduce road deaths significantly, since these levels now correspond to the major fraction of fatal crashes.