Quality of Service (QoS) is the manipulation of traffic such that a network device, such as a router or switch, forwards it in a fashion consistent with the required behaviors of the applications generating that traffic. In other words, QoS enables a network device to differentiate traffic and then apply different behaviors to the traffic.
The best way of deploying QoS is using bandwidth guarantees/rate limiting. Depending on the capabilities of the device, you may be able to define the Press8 IPs as having a guarantee (our subnet is 188.8.131.52/22), or you might need to try limiting non-voice traffic (such as port 80, 25, etc.), and specifying a rate-limit there. Using VLANs of course can also help you determine these classes for applying bandwidth rules to. The Polycom phones support 802.1q tagging. Last, if available bandwidth is slim at the customer location, we can use low-bandwidth audio codecs on the phones, specifically G.729, resulting in approx 32kbps up/down per call as opposed to ~95kbps for G711/G722.
One thing to check on the router is whether or not it is SIP-aware, as they generally cause more harm than good, and we pretty well always look for this and disable it where applicable. This is usually referenced as a SIP ALG (application layer gateway) on the router. It can also be helpful to disable deep packet inspection filters, may also be labeled as SPI / Stateful Packet Inspection. This prevents the routers from incorrectly identifying/filtering legitimate SIP traffic.