  Moduli spaces of holomorphic disks in a complex manifold Z, with boundaries
constrained to lie in a maximal totally real submanifold P, have recently been
found to underlie a number of geometrically rich twistor correspondences. The
purpose of this paper is to develop a general Fredholm regularity criterion for
holomorphic curves-with-boundary, and then show how this applies, in
particular, to various moduli problems of twistor-theoretic interest.
