A serious fairness problem occurs whenever homogeneous, finite buffer statistical multiplexer. Namely, the cell loss ratio performance varies widely across individual traffic streams. The cause of the problem is the particular random relation of the periodic frame transmission epochs of the video sources that feed the multiplexer. In this paper a protocol is pre- sented which controls the frame transmission epochs, in or- der to achieve fair distribution of losses among the admitted connections. The protocol operates with the participation of the sources by imposing an additional per-source delay on the traffic entering the network. These additional delays are calculated whenever a connection is accepted or termi- nated. The overall additional delay imposed by the protocol is guaranteed to be minimal through the use of an appropri- ate optimization algorithm. The performance of the proposed protocol, operating in conjunction with the optimization al- gorithm, is simulated and evaluated. A basic framework is given for its implementation on an ATM network. Finally, the issues of buffer overhead and the impact of the protocol on the delay experienced at the multiplexer are also discussed.