  We show the existence of strictly almost-Kahler anti-self-dual metrics on
certain 4-manifolds by deforming scalar-flat Kahler metrics.
  On the other hand, we prove the non-existence of such metrics on certain
other 4-manifolds by means of Seiberg-Witten theory. In the process, we provide
a simple new proof of the fact that any almost-Kahler anti-self-dual 4-manifold
must have a non-trivial Seiberg-Witten invariant.
