  We study the stability of the gauge hierarchy in hidden-sector supergravity
theories. We show that a destabilizing tadpole can appear if a theory has a
gauge- and global-symmetry singlet with renormalizable couplings to the visible
fields. We also find a quadratically divergent two-loop contribution to the
supersymmetric effective potential. This term illustrates the difficulty of
using the "LHC mechanism" to control quadratic divergences in theories with
Planck-scale vevs.
