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Many video compression algorithms require decisions to be made to select between different coding modes. In the case of H.264, this includes decisions about whether or not motion compensation is used, and the block size to be used for motion compensation. It has been proposed that constrained optimization techniques, such as the method of Lagrange multipliers, can be used to trade off between the quality of the compressed video and the bit rate generated. In this paper, we show that in many cases of practical interest, very similar results can be achieved with much simpler optimizations. Mode selection by simply minimizing the distortion with motion vectors and header information produces very similar performance to the full constrained optimization, while it reduces the mode selection and over all encoding time by 31% and 12%, respectively. The proposed approach can be applied together with fast motion search algorithms and the mode filtering algorithms for further speed up.