This paper discusses a new approach to QoS routing, introducing the notion of algorithm resilience (i.e., its capability to adapt to network and load modifications) as the performance index of the algorithm itself, for a given network topology, load and traffic pattern. The new approach can be summarized as network graph reduction, i.e., a modification of the graph describing the network before the routing path is computed, in order to exclude from the path selection over-congested portions of the network. This solution leads to a class of two-step routing algorithms, where both steps are simple, hence allowing efficient implementation. Simulation experiments, run on randomly-generated topologies and traffic patterns, show that these routing algorithms outperform both the standard minimum hop algorithm and those QoS-based algorithms based on the same metrics but not using the notion of network graph reduction.