To study the fundamental limits on the joint trans- mission of data of different levels of sensitivity, we establish the deterministic-code capacity region of a network with one transmitter and two receivers: an “ordinary receiver” and a “robust receiver.” The channel to the ordinary receiver is a given (known) discrete memoryless channel, whereas the channel to the robust receiver is an arbitrarily varying channel. Both receivers are required to decode the “common message” (the more sensitive data), whereas only the ordinary receiver is required to decode the “private message” (the less sensitive data).