In opportunistic routing the next relay is selected at each hop of each packet depending on the local pattern of simultaneous transmitters. The protocol considered in this paper assumes that at each hop, the optimal relay is chosen in a greedy way such that the packet receiver minimizes the remaining distance to the destination. The selection between potential relays is done using a logarithmic scale. This is a more efficient solution than the usually proposed solutions that use a linear scale.We evaluate the benefits of this protocol in the context of the point-to-point traffic in Vehicular Ad hoc NETworks (VANETs). We conduct this evaluation using extensive simulations with two widely used medium access techniques: slotted Aloha and CSMA.We show that even in one-dimensional scenarios, this protocol significantly outperforms conventional shortest path routing, offering shorter mean end-to-end packet delivery delay and smaller channel utilization