Controlling the bit-rate of video streams has become a key task in multimedia communication and broadcasting. In this work, we introduce an optimized video transcoder based on the systematic properties of the requantization process. Our method selects the optimal requantization step for each macroblock of the MPEG coding system, which leads to minimal transcoding errors. Moreover, we propose a new bit allocation algorithm that accounts for the drift errors in open loop transcoders, while maintaining low computational complexity and a low bit budget. We test our proposed algorithm on coded video data, and evaluate the results. It is concluded that the new algorithm is more efficient than currently available transcoding approaches.