Abstract: A statistical multiplexing apparatus and method for generating and combining a plurality of encoded video bit streams. A storage device contains pre-stored a priori statistics indicative of the encoding complexity of the video signals from which the encoded video bit streams will be generated. The pre-stored a priori statistics may include inter-pixel differences in the same picture or between multiple pictures or pre-encoding a priori statistics generated during a preliminary encoding of the video signals. Examples of pre-encoding a priori statistics include the number of bits per picture at a given quantization level, an average quantization level, picture types, scene change locations and repeat field for one or more of the video bit streams. The video signals are applied to encoders which compress the signals in accordance with bit allocation decisions generated by a statistics computer.