A plurality of programs are statistically multiplexed using a statistical multiplexing (stat mux) system. Rchannel, a constant total bit rate for the plurality of programs, is determined. Cl,Ff,picTYpe, a complexity for each picture in the plurality of programs, is determined. Tl,Ff,picType, a bit allocation for each picture in the plurality of programs, is determined based on Cl,Ff,picTYpe and Rchannel. The plurality of programs are encoded using a plurality of encoders, a combined encoder buffer, and Tl,Ff,picType to form a plurality of variable bit rate (VBR) compressed bit streams. The plurality of VBR compressed bit streams are multiplexed to form a single constant bit rate (CBR) bit stream.