This paper introduces a cost-effective technique to deal with CMP coherence protocol requirements from the interconnection network point of view. A mechanism is presented to avoid the end-to-end deadlock that arises from the dependency chains created at the network interfaces between the different message types handled by coherence protocols. Our proposal is designed to guarantee a fraction of end-to- end bandwidth for the highest priority messages and makes it unnecessary to employ several virtual networks or complex mechanisms for dealing with the limited capacity of the endpoint buffers. The presented approach uses the Rotary Router as its starting point, extending the original mechanism for the routing- dependent deadlock to the message-dependent deadlock. We also propose a solution that guarantees point-to-point message ordering in this router, which is a common requirement in some coherence protocols. Results for synthetic and parallel applications show that the proposal improves the performance of previous solutions with a much lower hardware cost.