Reducing the size of IP routing tables is one of the most compelling scaling problems affecting the Internet because of massive growth of routing table entries, increased traffic, and the migration to 128 bit IPv6 addresses. Various algorithms for IP table minimization have been proposed in the literature both for a single and for multiple tables, also with the possibility of performing address reassignments. In this paper we first introduce two new compression heuristics, the BFM and its evolution called BFM-Cluster, that exploit address reassignments for the minimization of multiple routing tables, and then we experimentally evaluate their performances together with the already existing techniques. Since a main problem posed by the growth of the routing tables sizes is the consequent general increase of the table lookup time during the routing of the IP packets, the aim is twofold: to measure and compare the compression ratios of the different algorithms, and to estimate the effects of the compression on the lookup times by measuring the induced improvement on the time of the main algorithms and data structures for the fast IP address lookup from the original tables to the compressed ones. Our point is that the existing techniques are efficient in different situations, with BFM-Cluster heuristic outperforming all other ones.