  To explain the dark matter and the baryon asymmetry of the Universe, the
parameters of the $\nu$MSM (an extension of the Minimal Standard Model by three
singlet neutrinos with masses smaller than the electroweak scale) must be
fine-tuned: one of the masses should be in the ${\cal O} (10)$ keV region to
provide a candidate for the dark-matter particle, while two other masses must
be almost the same to enhance the CP-violating effects in the sterile neutrino
oscillations leading to the baryon asymmetry. We show that a specifically
defined global lepton-number symmetry, broken on the level of ${\cal O}
(10^{-4})$ leads to the required pattern of sterile neutrino masses being
consistent with the data on neutrino oscillations. Moreover, the existence of
this symmetry allows to fix the flavour structure of couplings of singlet
fermions to the particles of the Standard Model and indicates that their masses
are likely to be smaller than ${\cal O} (1)$ GeV, opening a possibility of
their search in decays of charmed, beauty and even $K$ or $\pi$-mesons.
