  We characterize exotic C*-algebras of twisted, principal \'etale groupoids,
together with the abelian subalgebra associated to the unit space, as precisely
being the inclusions "$A\subseteq B$" of C*-algebras in which $A$ is abelian,
regular, and satisfies the extension property (pure states extend uniquely to
$B$). When $B$ is moreover nuclear, we deduce that the corresponding opaque
ideal is trivial. As an application, we give a streamlined characterization of
Kumjian's C*-diagonals as the regular abelian subalgebras satisfying the
extension property with vanishing opaque ideal.
