In this paper we study the anonymity provided by generalized mixes that insert dummy traffic. Mixes are an essential component to offer anonymous email services. We indicate how to compute the recipient and sender anonymity and we point out some problems that may arise from the intuitive extension of the metric to take into account dummies. Two possible ways of inserting dummy traffic are discussed and compared. An active attack scenario is considered, and the anonymity provided by mixes under the attack is analyzed.