  We show that requiring unbroken supersymmetry everywhere in black-hole-type
solutions of N=2,d=4 supergravity coupled to vector supermultiplets ensures in
most cases absence of naked singularities. We formulate three specific
conditions which we argue are equivalent to the requirement of global
supersymmetry. These three conditions can be related to absence of sources of
NUT charge, angular momentum, scalar hair and negative energy, although the
solutions can still have globally defined angular momentum and non-trivial
scalar fields, as we show in an explicit example. Furthermore, only the
solutions satisfying these requirements seem to have a microscopic
interpretation in String Theory since only they have supersymmetric sources.
These conditions exclude, for instance, singular solutions such as the
Kerr-Newman with M=|q|, which fails to be everywhere supersymmetric.
  We also present a re-derivation of several results concerning attractors in
N=2,d=4 theories based in the explicit knowledge of the most general solutions
of the timelike class.
