Trade-off curves for the exact and the relaxed QoS routing problem are presented and discussed. In addition, an efficient parametric linear programming algorithm to compute the trade-off curve of the relaxed problem is given. Trade-off curves enable a network operator to choose the set of constraints according to its QoS portfolio and are useful in the design of the network. In particular, the trade-off curves represent for the operator’s network the possible basic feasible solutions that can be computed rapidly. In some sense, we reverse the QoS routing problem by giving the network operator the means to advertise an appropriate set of QoS constraints for its network. Instead of offering the user the freedom to require desirable endto-end QoS levels from the operator, the user now can choose from the advertised QoS constraints portfolio those that best fit his application. The trade-off curve of the approximate, relaxed problem also gives insight in the computational complexity of QoS routing.