The Discrete Element Method (DEM) is a commonly used tool for simulating particulate behaviours over time. DEM covers two fundamental bases: the soft-sphere and hard-sphere methods. Existing hard-sphere DEM applies collisions as sequential ordered binary collisions that satisfy momentum conservation and a restitution coefficient: multiple collisions occurring within a single simulation iteration are ordered such that collisions may then be applied in the sequential binary instantaneous manner. It is proposed that multiple intra-time-step collisions be instead applied by averaging the outcomes of all collisions for each particle as detected at the beginning of the iteration, reducing the computational burden of the method. This averaged hard-sphere DEM was compared to soft-sphere DEM with a linear contact-stiffness model yielding an equivalent restitution coefficient for two two-dimensional scenarios, one resulting in transient dilute material behaviour and the other in steady dense material behaviour. The algorithm applying each DEM was written such that direct comparison of the computational time costs of each could be made. The simulation results suggest that significant computational time cost savings are available for simulation of dilute phase materials when applying the averaged hard-sphere DEM, in particular where the physical particle properties require a small time step of soft-sphere DEM. (C) 2009 Elsevier B.V. All rights reserved.