A plurality of programs are statistically multiplexed using a plurality of two-pass encoders. Pictures in the plurality of programs are encoded in a first encoding pass using a plurality of first encoding modules. RW—passOne, which is a total number of bits used to encode all the pictures in a sequence in the plurality of programs in the first encoding pass, is determined. RW—passTwo, which is a total target number of bits for all pictures in a same sequence in the plurality of programs in a second encoding pass, is also determined. Rtwo,Ff,picType(i,l), which is a target bit allocation for each picture in each program l of the plurality of programs, is determined based on RW—passOne, RW—passTwo, and Rone,Ff,picType(i,l). Rone,Ff,picType(i,l) is a number of bits consumed for a corresponding picture in the first encoding pass. The plurality of programs are encoded using a plurality of second encoding modules and Rtwo,Ff,picType(i,l) in the second encoding pass to form a plurality of variable bit rate (VBR) compressed bit streams. Thereafter, the plurality of VBR compressed bit streams are multiplexed to form a single constant bit rate (CBR) bit stream.