A statistical multiplexer is provided with a series of encoders that encode media streams at different bitrates to reduce jitter. The encoded media streams are transmitted to a multiplexer over a network and experience jitter that is reduced by a de-jitter arrangement. The multiplexer rearranges a transmit time of select packets in select ones of the media streams received over the network when a total group bandwidth available on the transmission channel over which the multiplexed media stream is to be transmitted is less than a sum of the bandwidths of the media streams because of the jitter and de-jitter process experienced by the media streams. The rearranging causes the bandwidth of the multiplexed media stream to be no greater than the total group bandwidth of the transmission channel without exceeding a maximum bit rate at which each individual encoded media stream is configured.