The spatial resolution of an x-ray CCD detector was determined from the widths of the tungsten x-ray lines in the spectrum formed by a crystal spectrometer in the 58 to 70 keV energy range. The detector had 20 microm pixel, 1700 by 1200 pixel format, and a CsI x-ray conversion scintillator. The spectral lines from a megavolt x-ray generator were focused on the spectrometer's Rowland circle by a curved transmission crystal. The line shapes were Lorentzian with an average width after removal of the natural and instrumental line widths of 95 microm (4.75 pixels). A high spatial frequency background, primarily resulting from scattered gamma rays, was removed from the spectral image by Fourier analysis. The spectral lines, having low spatial frequency in the direction perpendicular to the dispersion, were enhanced by partially removing the Lorentzian line shape and by fitting Lorentzian curves to broad unresolved spectral features. This demonstrates the ability to improve the spectral resolution of hard x-ray spectra that are recorded by a CCD detector with well-characterized intrinsic spatial resolution.