This study presents an efficient quasi-binary search algorithm for vector quantisation (VQ). The proposed algorithm adopts a tree-structured VQ (TSVQ) with overlapped codewords (TSOC) to reduce computational complexity and enhance quantisation quality. This algorithm uses overlapped codewords to expand the scope of the search path to traverse more appropriate codewords. In the authors' speech experiment, compared with the full search VQ (FSVQ), the average computational savings for triangle inequality elimination (TIE), TSVQ and TSOC are 23.65, 88.63 and 59.43%, respectively. In this experiment, the quantisation accuracy of TIE, TSVQ and TSOC are 100, 46.61 and 99.16%, respectively. To further evaluate computations at each stage of the proposed algorithm, both speech and images are considered. With codebook sizes of 256, 512 and 1024, the corresponding optimal computational savings for images are 84.59, 91.08 and 93.51%, respectively, compared with the FSVQ. For speech, the optimal computational savings reached 59.43% for a codebook size of 128. The results indicate that the proposed algorithm can save a significant number of computations, depending on the size of codebook. The TSOC algorithm is a trade-off between TSVQ and TIE, which provides a satisfactory computation quality. Moreover, unlike the TIE method, our algorithm does not depend on the high correlation characteristics of signals to reduce the amount of computation, but the TIE method can be incorporated into our algorithm to dramatically reduce the amount of computation.