We study watermarking techniques based on Quantization IndexModulation for which sets of lattice quantizers Qm are used (LQIM). A recipe for constructing such quantizers Qm is proposed, where the size of these sets is variable, so that the payload is easily adaptable. We make a comparative study of 8 dimensional lattices with good quantizer properties, where the embedding is done in the wavelet domain. Along the way, the gap between the theoretical ideas behind QIM and practical systems using lattices is closed by extending techniques, such as dithered quantizers and distortion compensation, from the scalar case to LQIM.