This contribution considers the critical time increment (〖∆t〗_crit) to achieve stable simulations using particulate discrete element method (DEM) codes that adopt a Verlet-type time integration scheme. The 〖∆t〗_crit is determined by considering the maximum vibration frequency of the system. Based on a series of parametric studies, 〖∆t〗_crit is shown to depend on the particle mass (m), the maximum contact stiffness (Kmax), and the maximum particle coordination number (CN,max). Empirical expressions relating 〖∆t〗_crit to m, Kmax, and CN,max are presented; while strictly only valid within the range of simulation scenarios considered here, these can inform DEM analysts selecting appropriate 〖∆t〗_crit values.