  Weak gravitational lensing is considered to be one of the most powerful tools
to study the mass and the mass distribution of galaxy clusters. However, weak
lensing mass reconstructions are plagued by the so-called mass-sheet
degeneracy--the surface mass density \kappa of the cluster can be determined
only up to a degeneracy transformation \kappa \to \kappa' = \lambda \kappa + (1
-\lambda), where \lambda is an arbitrary constant. This transformation
fundamentally limits the accuracy of cluster mass determinations if no further
assumptions are made. We describe here a method to break the mass-sheet
degeneracy in weak lensing mass maps using distortion and redshift information
of background galaxies and illustrate this by two simple toy models. Compared
to other techniques proposed in the past, it does not rely on any assumptions
on cluster potential; it can be easily applied to non-parametric
mass-reconstructions and no assumptions on boundary conditions have to be made.
In addition it does not make use of weakly constrained information (such as the
source number counts, used in the magnification effect). Our simulations show
that we are effectively able to break the mass-sheet degeneracy for
supercritical lenses, but that for undercritical lenses the mass-sheet
degeneracy is very difficult to be broken, even under idealised conditions.
