  We consider a minimal left-right model with a Peccei-Quinn symmetry, where
generalised charge conjugation plays the role of the left-right symmetry. We
show how the spontaneous breaking of the Peccei-Quinn symmetry by a scalar
singlet can provide us with solutions not only to the strong CP and dark matter
problems but can also help to generate naturally suppressed off-diagonal CKM
elements and small neutrino masses via the inverse seesaw mechanism. For this,
we make use of an economical scalar sector composed of a bi-doublet, two
doublets and a singlet only. As a result of the new gauge bosons and neutrinos,
the neutrinoless double beta decay, as well as lepton flavour violating
processes, receives new contributions which can, in principle, become relevant
due to the low-scale nature of the inverse seesaw mechanism. The model can
easily accommodate all the current data on fermion masses and mixing even if
the left-right scale is only high enough to evade the current experimental
constraints.
