Research on Voice over IP (VoIP) in infrastructure wireless local area networks (WLANs) has shown that, because of the access mechanism, the access point severely limits the number of voice calls a WLAN can support. To address this problem we propose a new scheme based on the IEEE 802.11e quality of service (QoS) mechanism where a tradeoff between codec quality and priority is exploited to improve the number of calls that can be supported. In particular, we propose certain priority settings at the access point (AP) to encourage users to switch to a lower quality codec during periods of high contention and thus enable them to maintain the call. We develop a detailed analytical model to show the benefit of this scheme. Our analytical results are validated by extensive simulation and show that the voice capacity in the network can be significantly improved. Furthermore, by using the ITU-T E-model to assess the voice quality, we show that users with a lower quality codec can still maintain an acceptable level of quality using the proposed scheme.