In traffic safety applications for Vehicular ad hoc networks (VANETs), some warning messages have to be urgently disseminated in order to increase the number of vehicles receiving the traffic warning information. In those cases, redundancy, contention, and packet collisions due to simultaneous forwarding (usually known as the broadcast storm problem) are prone to occur. In the past, several approaches have been proposed to solve the broadcast storm problem in multi-hop wireless networks such as Mobile ad hoc Networks (MANETs). Among them we can find counter-based, distance-based, location-based, cluster-based, and probabilistic schemes, which have been mainly tested in non-realistic simulation environments. In this paper, we present the enhanced Street Broadcast Reduction (eSBR), a novel scheme specially designed to increase the percentage of informed vehicles and reduce the notification time; at the same time, it mitigates the broadcast storm problem in real urban scenarios. We evaluate the impact that our scheme has on performance when applied to VANET scenarios based on real city maps, and the results show that it outperforms previous schemes in all situations.