We consider a generalization of point-to-point communication where besides the intended receiver, one or more additional nodes observe a degraded version of the transmitted signal. These nodes would like to be disturbed as little as possible by the transmission, where the amount of disturbance is quantified in terms of entropy rate. This setting is motivated by the interference channel, where each transmitter needs to control his impact on the unintended receivers while maintaining reliable transmission to his communication partner.

We characterize the rate-disturbance region exactly for the discrete memoryless case with a single disturbed node. A special case of this result permits a concise converse proof for the capacity region of the injective deterministic interference channel of Costa and El Gamal. 

For the deterministic case with two disturbed nodes, we develop an inner bound to the rate-disturbance region. When combined with the recently developed interference decoding strategy, this bound yields a new achievable rate region for deterministic interference channels with three user pairs.