Abstract: We study a specific example of energy-driven coarsening in two space dimensions. The energy is \int |\nabla \nabla u |^2 + (1-|\nabla u|^2)^2; the evolution is the fourth order PDE representing steepest descent. This equation has been proposed as a model of epitaxial growth for systems with slope selection. Numerical simulations and heuristic arguments indicate that the standard deviation of u grows like t^{1/3}, and the energy per unit area decays like t^{-1/3}. We prove a weak, one-sided version of the latter statement: the time-averaged energy per unit area decays no slower than t^{-1/3}. Our argument follows a strategy introduced by Kohn and Otto in the context of phase separation, combining (i) a dissipation relation, (ii) an isoperimetric inequality, and (iii) an ODE lemma. The interpolation inequality is new and rather subtle; our proof is by contradiction, relies on recent compactness results for the Aviles-Giga energy.