Common experience shows that electrodeposited (ED) metallic films exhibit rough surfaces unless the electrochemical bath contains small quantities of molecular additives. We develop a formalism for describing the effects of additives on surface morphology evolution, which builds on that in a companion paper for the additive-free case. We demonstrate that the additives suppress the morphological instability that leads to roughening by preferentially accumulating near surface protrusions and blocking growth sites. Our chemically based model shows that additives which readily adsorb onto the surface and have a strong tendency to complex with the metal cations reduce the driving force for the instability and thus enhance leveling. Furthermore, polar additives provide an additional stabilizing effect, in accord with experimental observations. It is also shown that linearly stable growth can be achieved over a wide range of deposition flux at sufficiently large additive bulk concentrations. We predict the ED conditions necessary for growing flat films and demonstrate that these are in good agreement with experimental observations. (C) 2003 The Electrochemical Society.