We study the possibility to enhance the phase space density of non-interacting particles submitted to a classical laser field without spontaneous emission. We clearly state that, when no spontaneous emission is present, a quantum description of the particle motion is more reliable than semi-classical description which can lead to large errors especially if no care is taken to smooth structures smaller than the Heisenberg uncertainty principle. Whatever the definition of position-momentum phase space density, its gain is severely bounded especially when started from a thermal sample. More precisely, the maximum of the position-momentum phase space density, can only increase by a factor M for M -level particles. This bound comes from a transfer between the external and internal degrees of freedom. Therefore, it is impossible to increase the position-momentum phase space density in the same internal state.