  The so-called Unitary Gauge Puzzle is re-examined in the light of a set of
gauge dependence identities discovered by Kobes, Kunstatter and Rebhan. The
``puzzle'' is discovered to arise as an artifact of the gauge-variant and
off-shell nature of the Effective Potential. An explicit analysis of the scalar
sector of the Abelian Higgs model shows that the correct physical result is
obtained in all cases provided that the calculation is performed
self-consistently, and the result is evaluated on-shell.
