  The properties of null geodesic congruences (NGCs) in Lorentzian manifolds
are a topic of considerable importance. More specifically NGCs with the special
property of being shear-free or asymptotically shear-free (as either infinity
or a horizon is approached) have received a great deal of recent attention for
a variety of reasons. Such congruences are most easily studied via solutions to
what has been referred to as the 'good cut equation' or the 'generalization
good cut equation'. It is the purpose of this note to study these equations and
show their relationship to each other. In particular we show how they all have
a four complex dimensional manifold (known as H-space, or in a special case as
complex Minkowski space) as a solution space.
