A postprocessing technique for mixed finite-element methods for the Cahn-Hilliard equation is analyzed.Once the mixed finite-element approximations have been computed at a fixed time on the coarser mesh,the approximations are postprocessed by solving two decoupled elliptic problems on a finer grid (or higher-order space).The analysis presented here shows that this technique increases the convergence rate of both the concentration and the chemical potential approximations.