  Two particular classes of axion models are presented, each one yielding a
lower bound on the axion decay constant, based though on different
considerations. In the first class only some, and not all, of the right-handed
quarks have PQ charges, whereas in the second one the left-handed sector of the
same quarks is taken into account as well. In the first case we find that
bounds coming from astrophysics are significantly relaxed compared with those
for the DFSZ. As for the second class, the astrophysical constraints proved to
be less severe (with one exception), than those coming from FCNC processes.
