Linear equations used to approximate reflection coefficient-versus-angle curves are usually valid only for small seismic parameter changes across reflectors, and they are rather inaccurate close to the critical angle. These inaccuracies affect the quality of AVO analysis and cause systematic errors when estimating relative seismic-parameter variations at reflectors, especially for density. We present an optimal model-based approach to build more accurate linear AVO approximations. Their basis functions are calculated by applying singular value decomposition to realistic modeled AVO curves. By extending the validity range of linear approximations to larger angles, this approach helps when using information contained at near-critical offsets. It alsooffers several advantages in other situations. The basis functions of the new approximations are orthogonal. Their coefficients represent new AVO attributes that can be used either to classify AVO responses directly, or to obtain more accurate estimates of usual AVO attributes (intercept, gradient, and possibly a third coefficient). This leads to a better estimation of seismic-parameter contrasts at reflecting interfaces. These coefficients are naturally sorted in decreasing order of importance. Therefore, the proper number of terms in the proposed equations can be chosen easily to offer an optimal compromise between noise and the information carried by each coefficient. Synthetic tests confirm the robustness of the method. This flexible and robust approach will be particularly well adapted for three-parameter AVO analysis.