  Unstable homoepitaxy on rough substrates is treated within a linear continuum
theory. The time dependence of the surface width $W(t)$ is governed by three
length scales: The characteristic scale $l_0$ of the substrate roughness, the
terrace size $l_D$ and the Ehrlich-Schwoebel length $l_{ES}$. If $l_{ES} \ll
l_D$ (weak step edge barriers) and $l_0 \ll l_m \sim l_D \sqrt{l_D/l_{ES}}$,
then $W(t)$ displays a minimum at a coverage $\theta_{\rm min} \sim
(l_D/l_{ES})^2$, where the initial surface width is reduced by a factor
$l_0/l_m$. The r\^{o}le of deposition and diffusion noise is analyzed. The
results are applied to recent experiments on the growth of InAs buffer layers
[M.F. Gyure {\em et al.}, Phys. Rev. Lett. {\bf 81}, 4931 (1998)]. The overall
features of the observed roughness evolution are captured by the linear theory,
but the detailed time dependence shows distinct deviations which suggest a
significant influence of nonlinearities.
