We propose a framework for the low-energy realization of supersymmetry which is very predictive, but differs radically in its phenomenological implications from the supersymmetric Standard Model (minimal or otherwise). The proposal consists of a supersymmetric version of the large-extra-dimensions scenario, with the Standard Model living on a 3-brane, coupled to a bulk sector consisting of six-dimensional supergravity. This picture is motivated by a promising recent attempt (hep-th/0304256) to naturally understand the observed dark energy density, and this connection with dark energy prevents making the extra dimensions smaller than of order 5 μm. The resulting inability to change this size makes the model very predictive, and easily falsifiable within the near future. Being supersymmetric, it may plausibly be embedded into a more fundamental theory such as string theory, in which case an additional 4 compact dimensions may also be present having inverse radii at the TeV scale or higher. The model is close to, but consistent with, current experimental constraints. We outline possible phenomenological implications for particle physics (both at accelerators and elsewhere), for precision tests of gravity, for astrophysics and for cosmology. © 2004 Elsevier B.V. All rights reserved.