This paper evaluates the applicability to WMNs of dynamic backpressure routing strategies, which theoretically maximize throughput but can result in high end-to-end delays. We present a distributed and (quasi-)stateless routing protocol called DiPUMP (forwarDIng of Packets for distribUted resource consuMPtion). Unlike the theoretical form of the backpressure algorithm, DiPUMP does not require a centralized entity computing the routes for the whole network at any instant. Therefore, its distributed operation enables its implementation and deployment in practical WMNs. By taking routing decisions on a per-packet basis, DiPUMP is able to substantially improve aggregated throughput, while maintaining acceptable end-to-end delays. We compare DiPUMP with a tree-based protocol, which is taken as a representative protocol for topology-based strategies. NS-3 simulation results show that DiPUMP and tree-based routing behave similarly under light loads. However, under medium and high loads, DiPUMP provides better results in terms of aggregated throughput, delay, and fairness.