We discuss the use of lattice vector quantizers in conjunction with a quadtree-based sorting algorithm for the compression of multidimensional data sets, as encountered,for example, when dealing with hyperspectral imagery. An extension of the SPECK algorithm is presented that deals with vector samples and is used to encode a group of successive spectral bands extracted from the hyperspectral image original block. We evaluate the importance of codebook choice by showing that a choice of dictionary that better matches the characteristics of the source during the sorting pass has as big an influence in performance as the use of a transform in the spectral direction. Finally, we provide comparison against state-of-the-art encoders, both 2D and 3D ones, showing the proposed encoding method is very competitive, especially at small bit rates.