  Requiring the presence of a horizon imposes constraints on the physical phase
space. After a careful analysis of dilaton gravity in 2D with boundaries
(including the Schwarzschild and Witten black holes as prominent examples), it
is shown that the classical physical phase space is smaller as compared to the
generic case if horizon constraints are imposed. Conversely, the number of
gauge symmetries is larger for the horizon scenario. In agreement with a recent
conjecture by 't Hooft, we thus find that physical degrees of freedom are
converted into gauge degrees of freedom at a horizon.
