  We use analytic formulae obtained from a simple model of crystal growth by
molecular--beam epitaxy to determine step--edge barriers to interlayer
transport. The method is based on information about the surface morphology at
the onset of nucleation on top of first--layer islands in the submonolayer
coverage regime of homoepitaxial growth. The formulae are tested using kinetic
Monte Carlo simulations of a solid--on--solid model and applied to estimate
step--edge barriers from scanning--tunneling microscopy data on initial stages
of Fe(001), Pt(111), and Ag(111) homoepitaxy.
