I discuss a thermal model for the continuous X-ray emission from SN 1006, which is also applicable to other supernova remnants (e.g., Cas A, IC 443) where power-law tails are observed at the high-energy end of the X-ray spectrum. It is essentially an updated version of the work of Hamilton and company. The mechanism for producing high-energy continua is thermal bremsstrahlung at the reverse shock, where the electron temperature might be considerably higher than at the forward shock if collisionless heating can occur, and line emission in the ASCA bandpass can be suppressed if the shocked material is carbon. For reasonable values of electron density and temperature, such as might be produced by shocks, the observed X-ray spectra of SN 1006 can be simulated, but morphological arguments and the mass of C required present difficulties for this model. The interpretation of the observed power-law continuum in SN 1006 as synchrotron radiation from cosmic-ray electrons is unchanged. For the other remnants, though, the mechanism discussed here might be much more viable and should certainly be considered.