We present continued development of laterally graded multilayer mirrors (LGMLs) for a telescope design capable of measuring linear X-ray polarization over a broad spectral band. The multilayer-coated mirrors are used as Bragg reflectors at the Brewster angle. By matching to the dispersion of a spectrometer, one may take advantage of high multilayer reflectivities and achieve modulation factors near 100%. In Phase II of the polarimetry beamline development, we demonstrated that the system

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... s 100% polarized X-rays at 0.525 keV (Marshall et al. 2013) . In Phase III of the polarimetry beam-line development, we installed an LGML in the source to polarize a wide range of energies between 0.15 and 0.70 keV (Marshall et al. 2014 ). Here, we present results from continued development of the LGMLs to improve reflectivity in the band of interest, a blazed reflection grating that is suitable for a small flight instrument, and a new detector with a directly deposited optical blocking filter. We also present updated plans for a suborbital rocket experiment designed to detect a polarization level of better than 10% for an active galactic nucleus.