There is a very extensive literature on exotic propulsion technologies that might be feasible for space missions beyond the solar system in the distant future. The CERN Geant4 package is more powerful and capable than the simulation environment used up until now for studies of the most advanced types of propulsion. This talk reports results from work done in summer 2010 (in press at the Journal of Propulsion & Power) and more recently, in summer 2011. Our results suggest that in principle, much higher velocities can be reached than previously reported.