  We study an extension of the standard anomaly/gauge mediation scenario where
the messenger fields have direct interactions with an extra gauge singlet. This
realizes a phenomenologically viable NMSSM-like scenario free of the mu-b_mu
problem. Current cosmological constraints imply a small size for the
anomaly-mediation contributions, unless some source of R-parity violation is
permitted. In the latter case the allowed regions in the parameter space can be
substantially larger than in the corresponding gauge-mediation scenario.
