  We consider cases where the dark matter-nucleon interaction is naturally
suppressed. We explicitly show that by extending the standard model scalar
sector by a number of singlets, can lead to a vanishing direct detection cross
section, if some softly broken symmetries are imposed in the dark sector. In
particular, it is shown that if said symmetries are $SU(2)$ ($SU(N)$) and $U(1)
\times S_N$, then the resulting pseudo-Nambu-Goldstone bosons can constitute
the dark matter of the Universe, while naturally explaining the missing signal
in nuclear recoil experiments.
