We propose a novel approach to QoS for real-time traffic over wireless mesh networks, in which application layer characteristics are exploited or shaped in the design of medium access control. Specifically, we consider the problem of efficiently supporting a mix of Voice over IP (VoIP) and delay-insensitive traffic, assuming a narrowband physical layer with CSMA/CA capabilities. The VoIP call carrying capacity of wireless mesh networks based on classical CSMA/CA (e.g., the IEEE 802.11 standard) is low compared to the raw available bandwidth, due to lack of bandwidth and delay guarantees. Time Division Multiplexing (TDM) could potentially provide such guarantees, but it requires fine-grained network-wide synchronization and scheduling, which are difficult to implement. In this paper, we introduce Sticky CSMA/CA, a new medium access mechanism that provides TDM-like performance to real-time flows without requiring explicit synchronization. We exploit the natural periodicity of VoIP flows to obtain implicit synchronization and multiplexing gains. Nodes monitor the medium using the standard CSMA/CA mechanism, except that they remember the recent history of activity in the medium. A newly arriving VoIP flow uses this information to grab the medium at the first available opportunity, and then sticks to a periodic schedule, providing delay and bandwidth guarantees. Delay-insensitive traffic fills the gaps left by the real-time flows using novel contention mechanisms to ensure efficient use of the leftover bandwidth. Large gains over IEEE 802.11 networks are demonstrated in terms of increased voice call carrying capacity (more than 100% in some cases). We briefly discuss extensions of these ideas to a broader class of real-time applications, in which artificially imposing periodicity (or some other form of regularity) at the application layer can lead to significant enhancements of QoS due to improved medium access.