We consider the stability of a single step during epitaxial growth of a monolayer on a continuously supplied substrate in the presence of an imposed gradient in the deposition rate along the direction of growth. This allows control of instabilities that arise from asymmetries in the supply of atoms attaching from the upper and lower side of the step. We consider both a linear stability analysis of a mean-field terrace-step model and kinetic Monte-Carlo (KMC) simulation of an atomistic growth model. (c) 2006 Elsevier B.V. All rights reserved.