  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 show that the requirement of
global supersymmetry implies the absence of sources for NUT charge, angular
momentum, scalar hair and negative energy, for which there is no microscopic
interpretation in String Theory. These conditions exclude, for instance,
singular solutions such as the Kerr-Newman with M=|q|, which fails to be
everywhere supersymmetric. There are, nevertheless, everywhere supersymmetric
solutions with "global" angular momentum and non-trivial scalar fields. We also
present similar preliminary results in N=1,d=5 supergravity coupled to vector
multiplets.
