In a vector quantization (VQ) framework, one of the key problems in its practical applications is the encoding speed. In order to speed up VQ encoding process, it is most important to avoid computing unnecessary k-dimensional (k-D) real Euclidean distances for the obviously unlikely candidate codewords. The mean, the variance and the two partial sums of a k-D vector have already been proposed as the effective features in the previous works in order to realize a rejection to the unlikely codeword by using just a little computational cost. It is clear that the mean and the variance of a k-D vector are constant but the two partial sums of a k-D vector are not constant depending on how they have been constructed. Therefore, how to construct two better partial sums for fast VQ encoding becomes important. Instead of using fixed the first half vector and the second half vector criterion that has been introduced in the previous works, this paper proposes a new energy-maximum criterion to construct two better partial sums for a k-D vector. Mathematical analysis and experimental results confirmed that the proposed criterion is much more effective for fast VQ encoding compared to the fixed criterion used in the previous works. In addition, it is very easy to use the energy-maximum criterion in practice.