In this paper, I develop efficient tools to simulate trees with a fixed number of extant species. The tools are provided in my open source R-package TreeSim available on CRAN. The new model presented here is a constant rate birth-death process with mass extinction and/or rate shift events at arbitrarily fixed times 1) before the present or 2) after the origin. The simulation approach for case (2) can also be used to simulate under more general models with fixed events after the origin. I use the developed simulation tools for showing that a mass extinction event cannot be distinguished from a model with constant speciation and extinction rates interrupted by a phase of stasis based on trees consisting of only extant species. However, once we distinguish between mass extinction and period of stasis based on paleontological data, fast simulations of trees with a fixed number of species allow inference of speciation and extinction rates using approximate Bayesian computation and allow for robustness analysis once maximum likelihood parameter estimations are available.