Virtual paths facilitate the rapid movement of end-to-end traffic streams in an ATM network by keeping processing at intermediate nodes en route to the minimum. There may exist, however, some virtual paths in an ATM network with low volumes of traffic on them. Balancing between efficient utilization of transmission resources en route and keeping intermediate switching to the minimum, lightly loaded virtual paths are decomposed into at most two logical hops, which require only one intermediate switching for an end-to-end traffic stream. The decomposition procedure and data structure for efficient implementation are described. For a twenty-node network with between three and four hundred virtual paths, experimental results show that the average number of lightly loaded virtual paths that cannot be decomposed by our procedure is about 6.5. Work in progress and future work lie in simulating network performance and investigating improved network dimensioning techniques for direct and two-hop routes in ATM networks.