The problem of anonymous networking when an eavesdropper observes packet timings in a communication network is considered. The goal is to hide the identities of source-destination nodes, and paths of information flow in the network. One way to achieve such an anonymity is to use mixers. Mixers are nodes that receive packets from multiple sources and change the timing of packets, by mixing packets at the output links, to prevent the eavesdropper from finding sources of outgoing packets. In this paper, we consider two simple but fundamental scenarios: double input-single output mixer and double input-double output mixer. For the first case, we use the information-theoretic definition of the anonymity, based on average entropy per packet, and find an optimal mixing strategy under a strict latency constraint. For the second case, perfect anonymity is considered, and a maximal throughput strategy with perfect anonymity is found that minimizes the average delay.