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Traditional methods for evaluating the amount of anonymity afforded by various Mix configurations have depended on either measuring the size of the set of possible senders of a particular message (the anonymity set size), or by measuring the entropy associated with the probability distribution of the messages possible senders. This paper explores further an alternative way of assessing the anonymity of a Mix system by considering the capacity of a covert channel from a sender behind the Mix to an observer of the Mix’s output. Initial work considered a simple model [4], with an observer (Eve) restricted to counting the number of messages leaving a Mix configured as a firewall guarding an enclave with one malicious sender (Alice) and some other naive senders (Cluelessi’s). Here, we consider the case where Eve can distinguish between multiple destinations, and the senders can select to which destination their message (if any) is sent each clock tick.