  Most of the phenomenological studies of supersymmetry have been carried out
using the so-called minimal supergravity scenario, where one assumes a
universal scalar mass, gaugino mass, and trilinear coupling at M_{GUT}. Even
though this is a useful simplifying assumption for phenomenological analyses,
it is rather too restrictive to accommodate a large variety of phenomenological
possibilities. It predicts, among other things, that the lightest
supersymmetric particle (LSP) is an almost pure B-ino, and that the
mu-parameter is larger than the masses of the SU(2)_{L} and U(1)_{Y} gauginos.
We extend the minimal supergravity framework by introducing one extra
parameter: the Fayet--Iliopoulos D-term for the hypercharge U(1), D_Y. Allowing
for this extra parameter, we find a much more diverse phenomenology, where the
LSP is \tilde{\nu}_{\tau}, \tilde{\tau} or a neutralino with a large higgsino
content. We discuss the relevance of the different possibilities to collider
signatures. The same type of extension can be done to models with the gauge
mediation of supersymmetry breaking. We argue that it is not wise to impose
cosmological constraints on the parameter space.
