  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.
