  The inversion of a gravitational lens system is, as is well known, plagued by
the so-called mass-sheet degeneracy: one can always rescale the density
distribution of the lens and add a constant-density mass-sheet such that the,
also properly rescaled, source plane is projected onto the same observed
images. For strong lensing systems, it is often claimed that this degeneracy is
broken as soon as two or more sources at different redshifts are available.
This is definitely true in the strict sense that it is then impossible to add a
constant-density mass-sheet to the rescaled density of the lens without
affecting the resulting images. However, often one can easily construct a more
general mass distribution -- instead of a constant-density sheet of mass --
which gives rise to the same effect: a uniform scaling of the sources involved
without affecting the observed images. We show that this can be achieved by
adding one or more circularly symmetric mass distributions, each with its own
center of symmetry, to the rescaled mass distribution of the original lens. As
it uses circularly symmetric distributions, this procedure can lead to the
introduction of ring shaped features in the mass distribution of the lens. In
this paper, we show explicitly how degenerate inversions for a given strong
lensing system can be constructed. It then becomes clear that many constraints
are needed to effectively break this degeneracy.
