  The QCD axion needs not be an exact pseudoscalar for solving the strong CP
problem. Its imperfectness can play a profound role cosmologically. We propose
effective operators, where the Peccei-Quinn field linearly couples to Standard
Model particles, provide a dynamical solution to the domain wall problem that
prevails in post-inflationary axion models with discrete symmetry. Such
interactions generate a thermal potential that drives the axion field to a
universal value throughout the universe at high temperatures thus preventing
the birth of domain walls when the QCD potential switches on. We discuss
generic conditions for this mechanism to work and several concrete examples.
Combining with existing electric dipole moment and fifth force constraints, a
lower bound on the axion mass is obtained around $10^{-5}$\,eV. Our findings
make a strong case for complementary axion searches with both quality
preserving and violating interactions.
