The convective Cahn-Hilliard equation has gathered a lot of attention in recent years. While its solutions have been analyzed thoroughly, we show that within the context of quantum dot dynamics, a higher order convective Cahn-Hilliard equation brings along strong similarities in the solution structure. The parameter plane for stationary solutions highlights the familiar kinks and further multi-hump solutions. The coarsening rates from numerical simulations, where small pyramids vanish while bigger ones continue growing, are comparable, but show a large initial logarithmic regime for small deposition rates.