Speed limits are a well-known instrument to improve traffic safety. However, speed limits alone are not enough; there is need for enforcement of these limits. In this paper we analyze the existing Belgian fine structure for speeding offences. We make two observations. First, the fine increases with the severity of the violation. Secondly, the fine depends on the speeders' offence history. That fines increase with the level of violation is a basic result in the literature. However, the literature is mixed with respect to the relationship with the offence history. We focus on this last point. We confront two fine structures, both increasing with speed: a uniform fine and a differentiated fine, which depends on the offence history. Drivers differ in their propensity to have an accident and hence in their expected accident costs. Literature then prescribes that the fine for bad drivers should be higher than for good drivers. However the government does not know the type of the driver. We state that the number of previous convictions gives information on the type of the driver. We want to know which structure minimizes the welfare losses. The result depends on the strength of the relationship between the type and having a record. We illustrate this by means of a numerical example.