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This paper proposes novel scalable mesh coding designs exploiting the intraband or composite statistical dependencies between the wavelet coefficients. A Laplacian mixture model is proposed to approximate the distribution of the wavelet coefficients. This model proves to be more accurate when compared to commonly employed single Laplacian or generalized Gaussian distribution models. Using the mixture model, we determine theoretically the optimal embedded quantizers to be used in scalable wavelet-based coding of semiregular meshes. In this sense, it is shown that the commonly employed successive approximation quantization is an acceptable, but in general, not an optimal solution. Novel scalable intraband and composite mesh coding systems are proposed, following an information-theoretic analysis of the statistical dependencies between the coefficients. The wavelet subbands are independently encoded using octree-based coding techniques. Furthermore, context-based entropy coding employing either intraband or composite models is applied. The proposed codecs provide both resolution and quality scalability. This lies in contrast to the state-of-the-art interband zerotree-based semiregular mesh coding technique, which supports only quality scalability. Additionally, the experimental results show that, on average, the proposed codecs outperform the interband state-of-the-art for both normal and nonnormal meshes. Finally, compared with a zerotree coding system, the proposed coding schemes are better suited for software/hardware parallelism, due to the independent processing of wavelet subbands.