1. In a multi-stage vector quantization encoder comprising a plurality of consecutive vector quantization stages wherein each stage comprises a vector quantizer and an associated codebook containing a plurality of codevectors, there being a unique address associated with each codevector in the codebook of each stage, a method comprising the steps of: p1 (a) receiving a data vector indicative of a block of data to be compressed; (b) selecting a codevector from the codebook at an initial stage that most closely resembles the data vector, generating a residual vector, and proceeding directly to step (e) if a measure of quantization error at that stage satisfies a threshold value, but otherwise first performing the following steps (c) and (d); (c) at a next succeeding stage, selecting a codevector from the codebook at that stage that most closely resembles the residual vector from the immediately preceding stage, and generating another residual vector; (d) repeating said step (c) until a measure of quantization error at a particular stage satisfies the threshold value; and then (e) transmitting addresses of each codevector selected in said steps (b) and (c) to a remote location.