  We explore a new class of axion models in which some, but not all, of the
left-handed quarks have a Peccei-Quinn symmetry. These models are potentially
afflicted by flavour changing neutral currents. We derive the bounds on the
Peccei-Quinn symmetry-breaking scale from bounds on the $K^+\to \pi^+ a$
branching ratio, showing that in some cases they are even stronger than the
astrophysical ones, but still not strong enough to kill off the models.
