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.
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