We consider the problem of rate-distortion optimized streaming of packetized media over the Internet from a server to a client using rich acknowledgments. Instead of separately acknowledging each media packet as it arrives, the client periodically sends to the server a single acknowledgment packet, denoted rich acknowledgment, that contains information about all media packets that have arrived at the client by the time the rich acknowledgment is sent. Computing the optimal transmission policy for the server involves estimation of the probability that a single packet will be communicated in error as a function of the expected redundancy (or cost) used to communicate the packet. In this paper, we show how to compute this error-cost function, and thereby optimize the server's transmission policy, in this scenario.