Supernova remnants present an excellent opportunity to study the shockacceleration of relativistic particles. X-ray synchrotron emission fromrelativistic electrons should contain important information, butextracting it requires advances in models and observations. I present thefirst test of sophisticated synchrotron models against high resolutionobservations on SN 1006, the first and best example of synchrotron X-rayemission, which has been well observed at radio, X-ray and gamma-raywavelengths. Synchrotron emission can be limited at the highest energies by finite age,radiative losses or electron escape. Earlier calculations suggested thatSN 1006 was escape limited. I adapted an escape-limited synchrotron modelfor XSPEC, and demonstrated that it can account for the dominantlynonthermal integrated spectrum of SN 1006 observed by ASCA-GIS and RXTE while constraining the values of the maximum electron energy and otherparameters. Combined with TeV observations, the fits give a mean postshockmagnetic field strength of 9 microgauss and 0.7% of the supernova energyin relativistic electrons. Simultaneous thermal fits gave abundances farabove solar, as might be expected for ejecta but had not previously beenobserved. I created subsets of the escape-limited model to fit spatially resolvedASCA SIS observations. I found only small differences between thenortheast and southwest limbs. A limit of less than 9% was placed on theamount of nonthermal flux elsewhere in the remnant. Important findingsinclude the possibility that rolloff frequency may change across theremnant face, and ruling out cylindrical symmetry for SN 1006 along aNW/SE axis. These models have implications far beyond SN 1006. The only previousmodel available to describe X-ray synchrotron emission was a powerlaw.These new models are superior to powerlaws both for their robustconstraints and because they shed physical insight on the accelerationmechanism. As new instruments increase our spatial and spectral resolutionI predict many more remnants will be found with varying amounts of X-raysynchrotron emission, hidden along with thermal lines and continuum. Theability to separate thermal and nonthermal emission is essential tounderstanding both nonthermal emission as well as the thermal component.