The aim of introducing energy dispersive analysis into X-ray fluorescence analysis is to suppress background from the Bremsstrahlung spectrum and the characteristic radiation without an undue reduction of the signal. The variant under consideration uses linearly polarization radiation obtained after a Bragg reflection,under delta = 90/sup 0/. In an introductory part, Bragg reflection, fluorescence and strong radiation are considered quantitatively with respect to counting statistics and detection limits. In the experimental part two combinations are describe, of a Ta crystal with a Cr tube and of a Mo crystal with a Mo tube. Details of adjustment, sample preparation and calibration and detection limits are given. The pros and cons of the Ta/Cr and the Mo/Mo are contrasted and proposals for further improvements are given.