We present a broad class of supersymmetric models that preserve R-parity but lack missing energy signatures. These models have new light particles with weak-scale supersymmetric masses that feel SUSY breaking only through couplings to the MSSM. This small SUSY breaking leads to nearly degenerate fermion/boson pairs, with small mass splittings and hence small phase space for decays carrying away invisible energy. The simplest scenario has low-scale SUSY breaking, with missing energy only from soft gravitinos. This scenario is natural, lacks artificial tunings to produce a squeezed spectrum, and is consistent with gauge coupling unification. The resulting collider signals will be jet-rich events containing false resonances that could resemble signatures of R-parity violation. We discuss several concrete examples of the general idea, and emphasize gamma + jet + jet resonances, displaced vertices, and very large numbers of b-jets as three possible discovery modes.

12 pages, 4 figures