This contribution considers the critical time increment (Δtcrit) to achieve stable simulations using particulate discrete element method (DEM) codes that adopt a Verlet-type time integration scheme. The Δtcrit is determined by considering the maximum vibration frequency of the system. Based on a series of parametric studies, Δtcrit 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 Δtcrit 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 Δtcrit values.