  New realizations of the gravity-mediated SUSY breaking are presented
consistently with an R symmetry. We employ monomial superpotential terms for
the hidden-sector (goldstino) superfield and Kahler potentials parameterizing
compact or non-compact Kahler manifolds. Their scalar curvature may be
systematically related to the R charge of the goldstino so that Minkowski
solutions without fine tuning are achieved. A mild violation of the R symmetry
by a higher order term in the Kahler potentials allows for phenomenologically
acceptable masses for the R axion. In all cases, non-vanishing soft
SUSY-breaking parameters are obtained and a solution to the mu problem of MSSM
may be accommodated by conveniently applying the Giudice-Masiero mechanism.
