Adaptive hierarchical algorithms of vector quantization (VQ) for image coding are proposed. First the basic codebook is generated adaptively using adaptive VQ, then the quadruplets of codes/indices in the so-called zigzag order are coded into higher level (second and third levels) codes by creating the second- and third-level index codebooks to reduce the redundancy presented in the codes. Partially matched quadruplets are also encoded in the second and third layers using the index codebooks along with corresponding correction schemes. The third-layer encoding achieves a better compression ratio than a two-layer encoding scheme, which was shown to be optimal when partial encoding was not adopted. This three-layer coding scheme achieves better compression with no extra distortion and little extra computation. Experiments show encouraging results.