  The general scalar potential of D-dimensional massive sigma-models with eight
supersymmetries is found for $D=3,4$. These sigma models typically admit 1/2
supersymmetric domain wall solutions and we find, for a particular
hyper-K\"ahler target, exact 1/4 supersymmetric static solutions representing a
non-trivial intersection of two domain walls. We also show that the
intersecting domain walls can carry Noether charge while preserving 1/4
supersymmetry. We briefly discuss an application to the D1-D5 brane system.
