We consider a routing problem where we want to minimize the maximal relative congestion on the arcs of the network with a bounded number of paths.We explain how that minimax problem is linked with the search of approximate solutions obtained by successive shortest-path calculations based on exponential arc distance functions.We then study the complexity of the determination of the minimal number of paths supporting a feasible flow, an NP-hard problem. We show how the Flow deviation method can be adapted to include a control on the number of paths and show some numerical experiments on medium-size networks.