We propose a traffic engineering (TE) architecture to supply wireless mesh networks (WMNs) with an efficient support of diverse applications with different quality of service (QoS) requirements. The proposed TE-WMN architecture is based on the MPLS technology. Its main goal is to provide TE capabilities so that a heterogeneous infrastructure, made of wired networks and WMNs, can be built and managed in a seamless manner. In the TE-WMN architecture, the path computation element (PCE) is in charge of finding a path that satisfies the QoS requirements. This operation often requires solving a multi-constrained problem, which is known to be NP-complete. So far many approximated and heuristic solutions have been developed for and applied to wired networks. However, the different features of WMNs make it impractical to reuse those solutions. Hence we have devised two heuristic path computation algorithms (PCAs) with the goal of keeping the complexity very low and yet improving the performance of simple existing algorithms. An extensive set of tests has proved the good performance of the proposed PCAs.