We propose a new compression-based algorithm that combines compression using lattice vector quantization (LVQ) in the wavelet domain and data hiding. It deals with two major constraints. (1) compression must not degrade the embedded mark and (2) watermarking must not affect coding performances. Our approach is based on a new multidimensional dead zone that enables us to maintain a sparse representation of the quantized wavelet coefficients, as well as a constant-entropy insertion method. Furthermore, an algorithm to estimate the quantization parameters is proposed. It leads to both variable rate encoding and bit rate adapted data hiding.