We describe QoSMap, a novel approach for mapping overlay networks with stringent QoS requirements. QoSMap computes high quality overlay paths by utilizing direct underlay paths that fulfill the application’s topology and link-specific QoS requirements. It also improves application dependability by increasing resiliency against QoS failures under dynamic network conditions. The increased resiliency is achieved through the use of supplemental indirect paths which have a single intermediate node and which also meet application QoS requirements. For evaluation, we compared QoSMap with a simple QoS approach for overlay mapping. We compared the two approaches for fulfilling varying application requests with strict QoS requirements of latency and packet loss on PlanetLab. We observed that QoSMap yielded high quality overlays. Further, the use of indirect paths upon the QoS failure of the direct path avoided overlay reconfiguration and resulted in increased dependability and longer lifetime...