A new bit allocation technique between motion vectors and DCT coefficients between MPEG-2 encoding is presented. In MPEG-2 encoding, the differential between two neighboring motion vectors is losslessly encoded by a Huffman table. In order to adjust the bit allocation for the motion vectors, a motion vector smoothing approach is taken. The motion vectors are smoothed by a low pass filter when the bit allocation for motion vectors has to be reduced. An algorithm based on langrange multiplier used to achieve the optimal balance between the motion vector smoothing and the DCT co efficient quantization.