Vector quantization (VQ) is a simultaneous quantization of a sequence of samples or vector. This process allows to malee effective use of the interrelations among the different vector components and performance arbitrarily close to the ultimate rate-distortion can be achieved by VQ if the vector dimension is high enough. Nevertheless, the exponential growth in complexity forces the use of low -dimensionality VQ in practica! systems. In this case sorne kind of adaptation is necessary to obtain adequate performance. Adaptive Multistage VQ (AMSVQ) [1] is a simple method that allows to redesign the quantizer as it is used, thus increasing its robustness and performance. In this paper, it is shown the close relation between the proposed adaptation algorithm and the methods usually employed to design the vector quantizers. Then sorne results are presented in which the AMSVQ reduce the complexity and improve the performance of previous VQ-based schemes of quantizing the LPC parameters.