The lead myristate multilayer analyzer has provided a basis for a relatively simple and efficient spectroscopy for the low‐energy x‐ray emissions in the 20–80‐A˚ region (where conventional crystal spectroscopy and grazing incidence grating spectroscopy are generally inefficient). The percent reflectivity, the integrated coefficient of reflection, and the Bragg diffraction width of the lead myristate analyzer have been measured and found to be consistent with the predictions of a simple theoretical model for multilayer diffraction. This multilayer spectroscopy at large Bragg angles has a high efficiency (high instrument transmission) as compared to grazing incidence grating spectroscopy in this 20–80‐A˚ region. However, the resolution is limited to that set by the diffraction width of the lead myristate analyzer of about 1 eV. Because the collimator‐crystal broadening function can be precisely defined, a simple and effective deconvolution procedure can be applied with this multilayer spectroscopy to bring the resolution into the sub‐electron‐volt region. To demonstrate the efficiency of lead myristate spectroscopy in the 20–80‐A˚ region, spectra were measured and analyzed from x‐ray excited fluorescent sources which are characteristically of low intensity. (X‐ray excitation yields a minimum of background spectra and of radiation damage.) These include theL2,3atomic spectrum of argon and the C‐Kmolecular spectrum of CO2, both in the gas phase, and the Cl‐L2,3and O‐Kspectra from solid lithium perchlorate. Many samples undergo appreciable radiation‐induced chemical change during the exposure time that is required for measurement—even with an optimally fast spectrograph and with fluorescent excitation. A method has been developed to evaluate and to correct for radiation damage by distributing the exposure over an effectively large sample volume either by gas flow or by rotating through multiple samples during measurement. Several spectral scans were made on the LiClO4using six samples. The total exposure time for each data point in each scan was recorded which permitted an extrapolation into a ’’zero’’ exposure spectrum. Finally, Fe‐L2,3/O‐Kspectrum (from Fe2O3) in the 17–25‐A˚ region is presented to illustrate the effectiveness of the lead myristate analyzer in third‐order diffraction. For this multilayer, the third‐order diffraction efficiency is one‐third that of the first order and is nearly twice that of the second order for this wavelength region.