  We revisit a Dark Matter model with an extension of the Standard Model with
two real singlets $\chi$ and $\eta$ obeying a $Z_2 \otimes Z_2'$ symmetry,
where $Z_2'$ is broken spontaneously. While $\chi$ serves as a stable Dark
Matter candidate providing the relic density, the real $\eta$ field plays the
role of a light mediator. We study the viability of this model with respect to
Dark Matter self-interactions which may explain the density profiles observed
in dwarf galaxies up to scales of the size of our Milky Way. Moreover, the
Standard Model-like Higgs boson of the model has a tiny mixing with the
mediator field and appears to be consistent with current LHC data. In this
rather minimal extension of the Standard Model the mediator $\eta$ decays
naturally into Majorana neutrinos neither disturbing standard big bang
nucleosynthesis nor cosmic microwave background observations.
