In one embodiment, a device in a shared-media communication network determines a priority of a packet to be queued at the device, and based on the priority determines a length of time the packet is allowed to be queued before being successfully transmitted. After attempting to successfully transmit the queued packet within the shared-media communication network, in response to reaching a threshold amount of the length of time without having successfully transmitted the queued packet, the device may transmit a “shaping” request to one or more reachable neighbors in the shared-media communication network. Specifically, the shaping request is for a temporary reduction in bandwidth utilization by the reachable neighbors for traffic having a comparatively lesser priority than the priority of the packet.