The paper treats a piping system, where the layout of the network is given but the diameters of the pipes should be chosen among a small number of different values. The cost of realizing the system should be minimized while keeping the energy heads at the nodes above some lower limits. A new algorithm using successive linear programming is presented. The performance of the algorithm is illustrated by optimizing a network with 201 pipes and 172 nodes. It is concluded that the new algorithm seems to be very efficient and stable, and that it always finds a solution with a cost near the best possible.