We examine the properties of relic neutralinos in the regions of the p
arameter space selected by recent fits to all the electroweak observab
les within the Minimal Supersymmetric Standard Model, We discuss the r
elic neutralino cosmic abundance and the direct detection rates for th
ese most likely supersymmetric configurations, We employ the relevant
experimental bounds to constrain the set of the best-fit configuration
s and discuss the discovery potential of the direct search for relic n
eutralinos.