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The standard lore has it that supersymmetry breaking in the visible sector is always soft when mediated by gravity from a hidden sector of Supergravity.Correspondingly, the associated generic forms of the superpotential and Kahler potential have long been the basis for the construction of consistent low energy susy models. In this talk we report on the existence of a whole class of new forms, equally consistent for low energy susy model building, but exhibiting hard susy breaking on top of the usual soft one. Moreover, these new forms require Standard Model gauge singlet chiral superfields displaying specific structures and flat directions. We discuss briefly the possible phenomenological spin-offs regarding the 125GeV Higgs fine-tuning issues and the (so far) non-discovery of susy particles, as well as next-to-minimal susy inflationary model-building. (based on G. Moultaka, M.R. de Traubenberg & D. Tant, Int.J.Mod.Phys. A34 (2019) no.01, 1950004, and work in progress).