The main new features in the Space Debris Mitigation long-term analysis program (SDM) recently upgraded to Version 4.0 are described. They include new or upgraded orbital propagators, two new collision probability algorithms, upgraded mitigation scenarios and new post-processing routines. The results of a set of simulations of the long term evolution of the Low Earth Orbit (LEO) environment are decribed. A No Future Launches, a Business as Usual and a Mitigated scenario are simulated, showing the need to adopt all the feasible proposed mitigation measures, in order to reduce the proliferation of orbiting debris. In particular, the mitigation measures proposed in this study appear capable of strongly reducing the growth of the 10 cm and larger population, but not enough to fully stabilize critical regions, such as the shell in the 800-1000 km altitude range.