Recent experimental studies confirm the prevalence of the widely known performance anomaly problem in current Wi-Fi networks, and report on the severe network utility degradation caused by this phenomenon. Although a large body of work addressed this issue, we attribute the refusal of prior solutions to their poor implementation feasibility with off-the-shelf hardware and their imprecise modelling of the 802.11 protocol. Their applicability is further challenged today by very high throughput enhancements (802.11n/ac) whereby link speeds can vary by two orders of magnitude. Unlike earlier approaches, in this paper we introduce the first rigorous analytical model of 802.11 stations' throughput and airtime in multirate settings, without sacrificing accuracy for tractability. We use the proportional-fair allocation criterion to formulate network utility maximisation as a convex optimisation problem for which we give a closed-form solution. We present a fully functional light-weight implementation of our scheme on commodity access points and evaluate this extensively via experiments in a real deployment, over a broad range of network conditions. Results demonstrate that our proposal achieves up to 100% utility gains, can double video streaming goodput and reduces TCP download by 8 x x. (C) 2015 Elsevier B.V. All rights reserved.