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Anonymous communications systems generally trade off performance for strong cryptographic guarantees of privacy. However, a number of applications with moderate performance requirements (e.g., chat) may require both properties. In this paper, we develop a new architecture that provides provably unlinkable and efficient communications using a single intermediary node. Nodes participating in these Mix-In-Place Networks (MIPNets) exchange messages through a mailbox in an Oblivious Proxy (OP). Clients leverage Secure Function Evaluation (SFE) to send and receive their messages from the OP while blindly but reversibly modifying the appearance of all other messages (i.e., mixing in place) in the mailbox. While an Oblivious Proxy will know that a client participated in exchanges, it can not be certain which, if any, messages that client transmitted or received. We implement and measure our proposed design using a modified version of Fairplay and note reductions in execution times of greater than 98% over the naïve application of garbled circuits. We then develop a chat application on top of the MIPNet architecture and demonstrate its practical use for as many as 100 concurrent users. Our results demonstrate the potential to use SFE-enabled "mixing" in a single proxy as a means of providing provable deniability for applications with near real-time performance requirements.