The integrator SSS performs accurate N -body simulations of the Solar System when there is a mix of massive bodies and test particles. The orbital motion of all bodies at all times is integrated using a 12-10 explicit Runge-Kutta Nyström (RKN) pair. The test particles are divided into sets and each set integrated on a different processor. The explicit RKN pair uses an order 12 interpolant for the position and velocity when checking for collisions. We report on two significant improvements to SSS. The first improvement reduced the local round-off error in interpolated values by approximately four orders of magnitude, permitting more accurate modelling of collisions. The technique used to reduce the round-off error can be applied to other high-order interpolants. The second improvement is hand optimization of the implementation of SSS. This optimization increased the speed of SSS by approximately 60%, permitting more accurate modelling through the use of more test particles. We also present a summary of the numerical performance of SSS on a simulation of the Sun, the planets Earth to Neptune, and 500,000 test particles over 100 million years.