Recent observations with the ASCA satellite (Koyama et al. 1995) have finally settled the question of the nature of the X-ray spectrum from the remnant of the supernova of 1006 AD. The bright rims have a featureless power-law spectrum while fainter parts of the remnant show a normal thermal spectrum with the expected lines. I describe model images and spectra that fit the data from the bright rims well, on the premise that the X-rays are synchrotron emission from electrons with energies up to 100 TeV accelerated in the remnant blast wave. The maximum energy to which electrons can be accelerated is limited by the requirement that the acceleration time be less than the smaller of the remnant age or the electrons' radiative loss time. In addition, absence of magnetohydrodynamic waves with sufficiently long wavelength to scatter electrons above some energy would allow electrons to escape freely above that energy, rather than being further accelerated. The maximum energy is thus a function of time and position. I assume that the electron mean free path is proportional to gyroradius, with proportionality constant f. With no internal magnetic field amplification beyond the original shock compression, the observed morphology, spectral shape, and X-ray flux at 4 keV can be fitted well with two models, one with escape, and the other with a perhaps unreasonably low upstream magnetic field. The former model has an external magnetic field strength of 3 mu G, f = 10, and a maximum MHD wavelength of 1017 cm. The latter, no-escape model has an external magnetic field strength of 0.6 mu G and f = 1. Both models predict upstream emission at a level of a few percent of postshock emission, but with differing morphologies. Models with an upstream magnetic field of 3 mu G and without escape overpredict X-rays at 4 keV by over an order of magnitude.