The Rocket Experiment Demonstration of a Soft X-ray Polarimeter (REDSoX) is a NASA-funded sounding rocket instrument that will make the first measurement of the linear X-ray polarization of an astrophysical source in the 0.2-0.4 keV band. We employ multilayer-coated mirrors as Bragg reflectors at the Brewster angle. By matching the dispersion of a dispersive spectrometer using critical angle transmission gratings to three laterally graded multilayer mirrors (LGMLs), we achieve polarization modulation factors over 90\%. We describe the potential science, the instrument, and possible extensions of the design.