  We provide a general strategy to obtain the superpotential W for both BPS and
non-BPS extremal black holes in N=2 four dimensional supergravities based on
symmetric spaces. This extends the construction of W in terms of U-duality
invariants that was presented in previous work on the $t^3$ model. As an
application, we explicitly provide W and the solutions to the related gradient
flows for the $st^2$ and stu models. The procedure is shown to hold also for
the full N=8 theory. The role of flat directions in moduli space is clarified.
