A kinetic theory of nucleation is modified to describe formation of clusters on surfaces bombarded by epithermal atoms (defined here as having insufficient energy to create sites leading to heterogeneous nucleation), accounting for enhanced (non-thermal) emission of particles from clusters and for formation of vacancy-adatom pairs. A potential function is given for the kinetic Gibbs-Thompson equation which yields the critical cluster size, and closed form expressions are obtained (in the steady-state approximation) for the rate of formation of supercritical clusters, and the non-equilibrium cluster-size distribution. The modified theory is combined with a simple model of a growing 2-D surface to demonstrate conditions for suppressing formation of stable clusters. Some prior applications of nucleation theory to epithermal bombardment are reviewed and extended, and a simple estimate is obtained for the epithermal Aux which suppresses the nucleation rate (to a particular arbitrary degree) which is subject to experimental verification. Prospects for realizing improved yield in interface-structure-sensitive electronic devices are discussed.