  Several theoretical motivations point to ultralight QCD axions with large
decay constants $f_a \simeq \mathcal{O}(10^{16}-10^{17})$ GeV, to which
experimental proposals are dedicated. This regime is known to face the problem
of overproduction of axion dark matter from the misalignment mechanism unless
the misalignment angle $\theta_{\rm mis}$ is as small as
$\mathcal{O}(10^{-3}-10^{-4})$, which is generally considered a fine-tuning
problem. We investigate a dynamical explanation for a small $\theta_{\rm mis}$.
The axion mass arises from strong dynamics and may be sufficiently enhanced by
early dynamics so as to overcome Hubble friction and drive the field value to
the bottom of the potential long before the QCD phase transition. Together with
an approximate CP symmetry in the theory, this minimum is very closely related
to today's value and thus $\theta_{\rm mis}$ can automatically be well under
unity. Owing to such efficient relaxation, the isocurvature perturbations are
essentially damped. As an existence proof, using supersymmetric theories we
illustrate that the Higgs coupling with the inflaton energy can successfully
achieve this axion damping in a consistent inflationary cosmology.
