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In this paper, we propose a powerful bit allocation that optimizes the quantization of the normal mesh geometry. This bit allocation aims to minimize the surface-to-surface distance [P. Cignoni et al., 1998] between the original irregular mesh and the quantized normal one, according to a target bitrate. Moreover, to provide a fast bit allocation, we approximate this surface-to-surface distance with a simple criterion depending on the wavelet coefficient distributions, and we use theoretical models. This provides a fast and low-complex model-based bit allocation yielding results better than the recent state-of-the-art methods like [A. Khodakovsky and I. Guskov, 2002].