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. A necessary condition is that the forcing on sea ice varies slowly on the damping time scale, in which case an EVP solution may still approach a Viscous Plastic one, but on a time scale longer than a single external time step. In this case, the EVP method becomes very close to the recently proposed modified EVP (mEVP) method in terms of stability and simulated behavior. In a simple test case dealing with sea ice breaking under the forcing of a moving cyclone, the EVP method with an enlarged damping time scale can simulate linear kinematic features which are very similar to those from the traditional EVP implementation, although a much smaller number of internal time steps is used. There is more difference in sea-ice thickness and linear kinematic features simulated in a realistic Arctic configuration between using the traditional and our suggested choices of EVP damping time scales, but it is minor considering model uncertainties associated with choices of many other parameters in sea-ice models.