  We demonstrate the potential of forthcoming mu -> e gamma and mu-e conversion
experiments to implicate or disfavor solutions to the gauge hierarchy problem
before the advent of the CERN Large Hadron Collider. Solutions of dynamical
electroweak symmetry breaking, little Higgs, supersymmetry, and extra
dimensions are considered. Correlations of mu -> e gamma and mu-e conversion
branching ratios are analyzed for discriminating patterns. Measurements of
these exotic muon decays may have compelling implications for supersymmetric
solutions.
