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Summary form only given. Based on an optimal estimate of the convergence rate of the second order norm, an improved error estimate for extraordinary Catmull-Clark subdivision surface (CCSS) patches is proposed. If the valence of the extraordinary vertex of an extraordinary CCSS patch is even, a tighter error bound and, consequently, a more precise subdivision depth for a given error tolerance, can be obtained. Furthermore, examples of adaptive subdivision illustrate the practicability of the error estimation approach.