  We examine the properties of relic neutralinos in the regions of the
parameter space selected by recent fits to all the electroweak observables
within the Minimal Supersymmetric Standard Model. We discuss the relic
neutralino cosmic abundance and the direct detection rates for these most
likely supersymmetric configurations. We employ the relevant experimental
bounds to constrain the set of the best-fit configurations and discuss the
discovery potential of the direct search for relic neutralinos.
