This paper presents an algorithm to perform the broadcasting of a packet to all the peers that are located into a convex region (Area of Interest) in a Voronoi based peer-to-peer network. The proposed algorithm is an advanced version of the compass routing algorithm, and it is able to guarantee the delivery of 100% of the packets, while minimizing the total number of packets that travel the network. The algorithm has been theoretically analyzed, and it has been implemented on a proof of concept peer-to-peer application, and experimental results show that the algorithm actually respects the reduced number of total packets used, as per the theoretical analysis.