We generalize the problem of controlling the interference created to an external observer while communicating over a discrete memoryless channel (DMC) which was studied in [1]. In particular, we consider the scenario where the transmission is established over a compound DMC channel with unknown state at both the encoder and the decoder. Depending on the exact state s of the channel, we ask for a different level of average precision Delta(s) on the establishment of the interference coordination with the external observer. For this setup, we fully characterize the capacity region.