In the latest years network virtualization and virtual routers have gained considerable attention, because with their aid it is possible to realize multiple virtual topologies on the same physical network. This plays a key role in cloud-based systems and VPN (Virtual Private Network), amongst others. In order to be able to forward IP packets according to multiple topologies, the router needs to store numerous Forwarding Information Bases (FIBs), which can lead to memory scalability issues. We address this issue by applying the well-known "trie-folding" FIB compression method to the case of multiple virtual FIBs (VFIBs). We propose two novel approaches to perform the compression, based on different virtual router architectures. We introduce a further opportunity for optimization, based on the distribution of next-hop labels. We formulate a minimization problem using entropy measure, and we provide a heuristic approach of solving the problem. We present numerical evaluations including lookup speed, memory size of compressed VFIBs, and their corresponding entropies. Based on these results and the underlying theoretical reasoning, we can safely say that the presented techniques are not only able to resolve the memory scalability issues of modern virtual routers, but they also improve lookup speed considerably, one of the most important performance measures in a core router, be it virtual or not.