  We study the Jones and Tod correspondence between selfdual conformal
4-manifolds with a conformal vector field and abelian monopoles on
Einstein-Weyl 3-manifolds, and prove that invariant complex structures
correspond to shear-free geodesic congruences. Such congruences exist in
abundance and so provide a tool for constructing interesting selfdual
geometries with symmetry, unifying the theories of scalar-flat Kahler metrics
and hypercomplex structures with symmetry. We also show that in the presence of
such a congruence, the Einstein-Weyl equation is equivalent to a pair of
coupled monopole equations, and we solve these equations in a special case. The
new Einstein-Weyl spaces, which we call Einstein-Weyl ``with a geodesic
symmetry'', give rise to hypercomplex structures with two commuting
triholomorphic vector fields.
