  Let $(M^4,g)$ be a smooth, closed, oriented anti-self-dual (ASD)
four-manifold. $(M^4,g)$ is said to be unobstructed if the cokernel of the
linearization of the self-dual Weyl tensor is trivial. This condition can also
be characterized as the vanishing of the second cohomology group of the ASD
deformation complex, and is central to understanding the local structure of the
moduli space of ASD conformal structures. It also arises in construction of ASD
manifolds by twistor and gluing methods. In this article we give conformally
invariant conditions which imply an ASD manifold of positive Yamabe type is
unobstructed.
