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��_��, \tilde�� 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.

11 pages, 1 figure, uses psfig