: The paper proposes a lossy compression mechanism for 3D models (3D meshes) by improving existing compression mechanism such as progressive meshes and single refinement mesh compression. The methodology proposes to use a data hiding mechanism - multilevel quantization index modulation (MQIM), which hides or compresses data within subset of the data set with high embedding rates per data sample and minimizes the distortion to the meaning of the data set. The paper estimates the bounds on the compression in terms of the hiding capacity offered by MQIM. Experimental results show that the proposed method can achieve a high compression ratio (0.3-0.5) on the encoded data stream with small distortion.