We present techniques for traffic engineering in quality of service (QoS)-supported data networks and also illustrate the application of these techniques in a case study For scalability, we use multicommodity flow (MCF) solution techniques as primitives. The techniques address the design of topology and size of explicit routes in multiprotocol label switching (MPLS)-supported Internet protocol (IP) networks and virtual private networks (VPNs). The techniques are for network-wide optimization, subject to constraints on routing imposed by end-to-end QoS and other considerations. The notion of admissible route sets is used to differentiate real-time services such as Internet telephony and video, from delay-insensitive services, such as premium data. Different optimization techniques are given for Best-Effort services. We also give an efficient and accurate design technique to handle priorities. Finally, we present a novel technique for obtaining traffic engineering designs for stochastic traffic models from MCF-based designs with only a small amount of incremental effort.