Significant progress has been made in understanding the behavior of TCP and congestion-controlled traffic over multi- hop wireless networks. Despite these advances, however, no prior work identified severe throughput imbalances in the basic scenario of mesh networks, in which one-hop flows contend with two-hop flows for gateway access. In this paper, we demonstrate via real network measurements, test-bed experiments, and an analytical model that starvation exists in such a scenario, i.e., the one-hop flow receives most of the bandwidth while the two- hop flow starves. Our analytical model yields a solution consisting of a simple contention window policy that can be implemented via mechanisms in IEEE 802.11e. Despite its simplicity, we demonstrate through analysis, experiments, and simulations, that the policy has a powerful effect on network-wide behavior, shifting the network's queuing points, mitigating problematic MAC behavior, and ensuring that TCP flows obtain a fair share of the gateway bandwidth, irrespective of their spatial locations.