  We investigate the stabilisation equations for sufficiently general, yet
regular, extremal (supersymmetric and non-supersymmetric) and non-extremal
black holes in four-dimensional N=2 supergravity using both the H-FGK approach
and a generalisation of Denef's formalism. By an explicit calculation we
demonstrate that the equations necessarily contain an anharmonic part, even in
the static, spherically symmetric and asymptotically flat case.
