The purpose of this paper is to introduce a new adaptive vector quantizer (VQ) which takes place in a temporal adaptative coding scheme for the compression of digital image sequences. Our approach, which has to perform a fast codebook construction, unifies both efficient coding methods: a fast lattice encoding and an unbalanced tree-structured codebook design according to a distortion vs. rate tradeoff. Moreover, this tree-structured lattice vector quantizer (TSLVQ) has a convenient property: because of its lattice structure, no reproduction vector has to be transmitted. Briefly this TSLVQ is based on the hierarchical packing of embedded truncated lattices. We investigate her its design: by, first, explaining how to determine the support lattice and secondly how to obtain the hierarchical set of truncated lattice structures which can be optimally embedded with respect to the hierarchical packing. We then use a simple quantization procedure and describe the coresponding tree-structures codebook. Finally we present two unbalanced tree-structured codebook design algorithms based on the BFOS distortion vs. rate criterion.