  We derive extremal black hole solutions for a variety of four dimensional
models which, after Kaluza-Klein reduction, admit a description in terms of 3D
gravity coupled to a sigma model with symmetric target space. The solutions are
in correspondence with certain nilpotent generators of the isometry group. In
particular, we provide the exact solution for a non-BPS black hole with generic
charges and asymptotic moduli in N=2 supergravity coupled to one vector
multiplet. Multi-centered solutions can also be generated with this technique.
It is shown that the non-supersymmetric solutions lack the intricate moduli
space of bound configurations that are typical of the supersymmetric case.
