Simulations of the dynamics of biomolecules have been greatly accelerated by the use of multiple time-stepping methods, such as the Verlet-I/r-RESPA (reversible reference system propagator algorithms) method, which is based on approximating "slow'' forces as widely separated impulses. Indeed, numerical experiments have shown that time steps of 4 fs are possible for these slow forces but unfortunately have also shown that a long time step of 5 fs results in a dramatic energy drift. To overcome this instability, a symplectic modification of the impulsive Verlet-I/r-RESPA method has been proposed, called the mollified impulse method. The idea is that one modifies the slow part of the potential energy so that it is evaluated at "time averaged'' values of the positions, and one uses the gradient of this modified potential for the slow part of the force. By filtering out excitations to the fastest motions, these averagings allow the use of longer time steps than does the impulse method. We introduce a new mollified method, Equilibrium, that avoids instability in a more effective manner than previous averaging mollified methods. Our experiments show that Equilibrium with a time step of 6 fs is as stable as the impulsive Verlet-I/r-RESPA method with a time step of 4 fs. We show that it may be necessary to include the effect of nonbonded forces in the averaging to make yet longer time steps possible. We also show that the slight modification of the potential has little effect on accuracy. For this purpose we compare self-diffusion coefficients and radial distribution functions against the Leapfrog method with a short time step (0.5 fs).