  We derive simple and explicit expressions for the high frequency spectrum of
a classical accretion disc. Both stress-free and finite stress inner boundaries
are considered. A classical accretion disc spectrum with a stress-free inner
boundary departs from a Wien spectrum at large $\nu$, scaling as $\nu^{2.5}$
(as opposed to $\nu^3$) times the usual exponential cut-off. If there is finite
stress at the inner disc boundary, the maximum disc temperature generally
occurs at this edge, even at relatively modest values of the stress. In this
case, the high frequency spectrum is proportional to $\nu^2$ times the
exponential cut-off. If the temperature maximum is a local hot spot, instead of
an axisymmetric ring, then an interior maximum produces a $\nu^2$ prefactor
while an edge maximum yields $\nu^{1.5}$. Because of beaming effects, these
latter findings should pertain to a classical relativistic disc. The
asymptotics are in general robust and independent of the detailed temperature
profile, provided only that the liberated free energy of differential rotation
is dissipated locally, and may prove useful beyond the strict domain of
classical disc theory. As observations continue to improve with time, our
findings suggest the possibility of using the high energy spectral component of
black hole candidates as a signature prediction of classical theory, as well as
an diagnostic of the stress at the inner regions of an accretion disc.
