  We classify weak-scale extensions of the Standard Model which automatically
preserve its accidental and approximate symmetry structure at the
renormalizable level and which are hence invisible to low-energy indirect
probes. By requiring the consistency of the effective field theory up to scales
of 10^15 GeV and after applying cosmological constraints, we arrive at a finite
set of possibilities that we analyze in detail. One of the most striking
signatures of this framework is the presence of new charged and/or colored
states which can be efficiently produced in high-energy particle colliders and
which are stable on the scale of detectors.
