Abstract: We consider a simple extension of the Standard Model by the addition of N real scalar gauge singlets $\vp$ that are candidates for Dark Matter. By collecting theoretical and experimental constraints we determine the space of allowed parameters of the model. The possibility of ameliorating the little hierarchy problem within the multi-singlet model is discussed. The Spergel-Steinhardt solution of the Dark Matter density cusp problem is revisited. It is shown that fitting the recent CRESST-II data for Dark Matter nucleus scattering implies that the standard Higgs boson decays predominantly into pairs of Dark Matter scalars. It that case discovery of the Higgs boson at LHC and Tevatron is impossible. The most likely mass of the dark scalars is in the range 15 GeV $\lsim \mvp \lsim$ 50 GeV with $BR(h \to \vp\vp)$ up to 96%.