A vector excitation coder compresses vectors by using an optimum codebook designed off line, using an initial arbitrary codebook and a set of speech training vectors exploiting codevector sparsity (i.e., by making zero all but a selected number of samples of lowest amplitude in each of N codebook vectors). A fast-search method selects a number N.sub.c of good excitation vectors from the codebook, where N.sub.c is much smaller thaORIGIN OF INVENTIONThe invention described herein was made in the performance of work under a NASA contract, and is subject to the provisions of Public Law 96-517 (35 USC 202) under which the inventors were granted a request to retain title.