  Specialising to the case of Kerr-Schild spacetimes, which include the Kerr
black hole and gravitational wave solutions, we propose a modification of the
Penrose quasi-local energy. The modification relies on the existence of a
natural Minkowski background for Kerr-Schild spacetimes. We find that the
modified surface integral reduces to a volume integral of the Einstein tensor,
which has been proposed previously as an appropriate definition for quasi-local
energy for Kerr-Schild backgrounds. Furthermore, in the special case that the
Kerr-Schild null vector is normal to the surface of interest, we construct a
1-1 map between the 2-surface twistors in the Kerr-Schild background and
Minkowski twistors projected onto the surface.
