  We study a class of gauge groups that can automatically yield a
perturbatively exact Peccei-Quinn symmetry, and we outline a model in which the
axion quality problem is solved at all operator dimensions. Gauge groups
belonging to this class can also enforce and protect accidental symmetries of
the clockwork type, and we present a toy model where an `invisible' axion
arises from a single breaking of the gauge and global symmetries.
