Often in Internet Protocol (IP) networks, links are assigned weights, and traffic demands are routed along shortest paths. Hence, these link weights are the parameters which determine the routing paths. This paper addresses the problem of dimensioning an IP network to the lowest possible cost. Thus, routing paths have to be optimized with respect to this economic objective. This is equivalent to defining suitable weights on the links. In real-life networks, the weights can be chosen among a large set of values (from 1 to 216 ). However, to make the optimization process as efficient and tractable as possible, we wish to restrict the number of possible weight values on arcs to only a few ones. Hence, we propose some rules for building small sets of weights adapted to our network design problem. Using a simulated annealing heuristic, numerical experiments are performed on several network topologies. They show the relevance of our theoretical analysis to build sets of weights. The opti...