Single crystalline Cu films are extensively used as buffer layers for a variety of applications. Cu films can be grown epitaxially on hydrogen-terminated Si(001) and (7 x 7) reconstructed Si(111) substrates but the ultimate surface of the "as-grown" films tends to be quite rough. For most applications this constitutes a technical drawback. Using correlated reflection high-energy electron diffraction (RHEED) and STM data, we have found a dramatic smoothing of epitaxial Cu(001) surfaces by annealing the as-grown films in the 120-160degreesC temperature range and somewhat less so for the Cu(111) films. Scaling analysis of the subsequent Cu growth on the annealed smooth surfaces yields a coarsening exponent of one-fourth for the (001) oriented films while this exponent is one-third for the (111) films, providing experimental data for a comparison of the same system filmy substrate in these two orientations. (C) 2002 Elsevier Science B.V. All rights reserved.