  The complex-shift method is applied to the Kuzmin-Toomre family of discs to
generate a family of non-axisymmetric flat distributions of matter. These are
then superposed to construct non-axisymmetric flat rings. We also consider
triaxial potential-density pairs obtained from these non-axisymmetric flat
systems by means of suitable transformations. The use of the imaginary part of
complex-shifted potential-density pairs is also discussed.
