A computer-implemented method for inspection of a sample includes defining a plurality of locations on a surface of the sample, irradiating the surface at each of the locations with a beam of X-rays, and measuring an angular distribution of the X-rays that are emitted from the surface responsively to the beam, so as to produce a respective plurality of X-ray spectra. The X-ray spectra are analyzed to produce respective figures-of-merit indicative of a measurement quality of the X-ray spectra at the respective locations. One or more locations are selected out of the plurality of locations responsively to the figures-of-merit, and a property of the sample is estimated using the X-ray spectra measured at the selected locations.