  Polchinski has argued that the prediction of Hawking radiation must be
independent of the details of unknown high-energy physics because the
calculation may be performed using `nice slices', for which the adiabatic
theorem may be used. If this is so, then any calculation using a manifestly
covariant --- and so slice-independent --- ultraviolet regularization must
reproduce the standard Hawking result. We investigate the dependence of the
Hawking radiation on such a short-distance regulator by calculating it using a
Pauli--Villars regularization scheme. We find that the regulator scale,
$\Lambda$, only contributes to the Hawking flux by an amount that is
exponentially small in the large variable ${\Lambda}/{T_\ssh} \gg 1$, where
$T_\ssh$ is the Hawking temperature; in agreement with Polchinski's arguments.
We also solve a technical puzzle concerning the relation between the
short-distance singularities of the propagator and the Hawking effect.
