We propose to make the damping time scale, which governs the decay of pseudo-elastic waves in the Elastic Viscous Plastic (EVP) sea ice solvers, independent of the external time step and large enough to warrant numerical stability for a moderate number of internal time steps. In this case, EVP becomes very close to the recently proposed modified EVP (mEVP) method in terms of stability. With the proposed damping time scale, the numerical stability of EVP is independent of mesh resolution in setups where the sea ice model component is called every time step of the ocean model. In a simple test case dealing with sea ice breaking under the action of a moving cyclone, EVP with specified damping time scales can produce linear kinematic features very similar to those from the mEVP method. There is more difference in simulated Arctic sea ice thickness and linear kinematic features in realistic configurations, but the difference is minor considering model uncertainties associated with parameter choices in sea ice models.