Internet users usually download more than they upload and many technologies have asymmetric bandwidth ― greater from servers to clients than from clients to servers. Suppose some clients want to send messages to a server. At any point, the server knows all the messages it has received so far; each client only knows its own message or messages and does not overhear communication between other clients and the server. Thus, the server may be able to compress the messages but the clients individually cannot. Adler and Maggs [2] assumed the server, after receiving a sample of messages, can accurately estimate the distribution of all the messages. They then gave a multi-round asymmetric communication protocol in which the server uses its greater bandwidth to help a single client send a message drawn from a distribution known to the server. The server can just repeat their protocol to help any number of clients, provided it starts with a representative sample.