Since the advent of the first IEEE 802.11 standard, several papers have proposed means of providing QoS to IEEE 802.11 networks and evaluate various traffic-prioritization mechanisms. Nevertheless, studies on the assignment of AIFS times defined in IEEE 802.11e reveal that the various priority levels work in a synchronized manner. The studies show that, under large loads of high-priority traffic, EDCA starves low-priority frames, which is undesirable. We argue that QoS traffic needs to be prioritized, but users sending best-effort frames should also obtain the expected service. High-priority traffic can also suffer performance degradation when using EDCA because of heavy loads of low-priority frames. Thus, we have proposed a mechanism based on desynchronizing the IEEE 802.11e working procedure. It prevents stations that belong to different priority classes from attempting simultaneous transmission, prioritizes independent collision groups and achieves better short-term and long-term channel access fairness. We have evaluated the proposal based on extensive analytical and simulation results. It prevents the strangulation of low-priority traffic, and, moreover, reduces the degradation of high-priority traffic with the increased presence of low-priority frames.