An X-ray spectroscope collects an energy-dispersive spectrum from a sample under analysis, and generates a list of candidate elements that may be present in the sample. A wavelength dispersive spectral collector is then tuned to obtain X-ray intensity measurements at the energies/wavelengths of some or all of the candidate elements, thereby verifying whether or not these candidate elements are in fact present in the sample. Additionally, the alignment of the wavelength dispersive spectral collector versus the sample can be optimized by tuning the wavelength dispersive spectral collector to the energy/wavelength of a selected one of the candidate elements—preferably one whose presence in the sample has been verified, or one which has a high likelihood of being present in the sample—and then varying the alignment of the wavelength dispersive spectral collector versus the sample until the wavelength dispersive spectral collector returns the maximum intensity reading for the selected candidate element. Intensity readings for the other candidate elements can then be collected at this optimized alignment.