A wireless network of consumer electronic (CE) devices in a modern home, is typically running streaming services with heterogeneous bandwidth demands. Satisfying these demands offers the challenge of mapping them efficiently onto scarce wireless channel bandwidth. This mapping is supported by the IEEE 802.11e standard which provides cooperative and competitive distributed control for bandwidth assignment through a set of medium access control (MAC) mechanisms. While these mechanisms leverage priority arbitration for wireless channel usage, they are typically configured without taking the knowledge of streaming services into account thus resulting in suboptimal bandwidth utilization. This paper presents a streaming-aware wireless channel utilization policy. For defining and understanding the policy, a previous analytic model, which focuses mainly on the aspect of obtaining control of the channel, is extended with the aspect of retaining control according to application requirements. The model is simpler than previous works; it is compared with simulations and shown to be accurate. A utilization improvement of up to 18% is observed to be possible showing that such cross-layer optimization improves resource use.