Considered are optimal dynamic policies for multiplexing Κ + 1 heterogeneous traffic types onto a single communication channel. The packet types arrive to the channel according to independent Poisson processes. The service requirements are exponential with type dependent means. The optimization criterion is to minimize a linear combination of the average delays for packet types 1 to Κ , while simultaneously subjecting the average delay of type-0 packets to a hard constraint. The optimal multiplexing policy is shown to be a randomized modification of the “ μc rule”. The optimization problem is thereby reduced to a problem of finding the optimal randomization factor; an algorithm, which can be implemented in real time, is given to do this for two particular cases.