The problem of finding and updating shortest paths in distributed networks is considered crucial in today's practical applications. In the recent past, there has been a renewed interest in devising new efficient distance-vector algorithms as an attractive alternative to link-state solutions for large-scale Ethernet networks, in which scalability and reliability are key issues or the nodes can have limited storage capabilities. In this paper we present Distributed Computation Pruning (DCP), a new technique, which can be combined with every distance-vector routing algorithm based on shortest paths, allowing to reduce the total number of messages sent by that algorithm and its space occupancy per node. To check its effectiveness, we combined DCP with DUAL (Diffuse Update ALgorithm), one of the most popular distance-vector algorithm in the literature, which is part of CISCO's widely used EIGRP protocol, and with the recently introduced LFR (Loop Free Routing) which has been shown to have good performances on real networks. We give experimental evidence that these combinations lead to a significant gain both in terms of number of messages sent and memory requirements per node.