A method for synthesising link-disjoint Virtual Paths (VPs) at minimum cost in ATM networks is described in [1]; in the minimum cost synthesis, a physical network topology is determined and transmission capacities are allocated to the VPs. In this paper, we extend the method to allow for a hop-limit constraint in the VP synthesis. To solve the problem of minimum cost VP synthesis subject to a hop-limit constraint, we have developed two effective heuristic methods for solving a hop-limited minimum cost flow problem with link-disjoint path constraints. The link cost functions are the sums of constant costs and variable (capacity dependent) costs. The methods are analysed and illustrated with examples.