  We explain when the first-order Hamilton-Jacobi equations for black holes
(and domain walls) in (gauged) supergravity, reduce to the usual first-order
equations derived from a fake superpotential. This turns out to be equivalent
to the vanishing of a newly found constant of motion and we illustrate this
with various examples. We show that fake supersymmetry is a necessary condition
for having physically sensible extremal black hole solutions. We furthermore
observe that small black holes become scaling solutions near the horizon. When
combined with fake supersymmetry, this leads to a precise extension of the
attractor mechanism to small black holes: The attractor solution is such that
the scalars move on specific curves, determined by the black hole charges, that
are purely geodesic, although there is a non-zero potential.
