In many cases, the preconcentration of impurities by matrix elimination for subsequent atomic emission or atomic absorption determinations in the analysis of high-purity substances does not provide the possible values of detection the limits of widespread elements because of the high values of blank corrections. The main sources of contaminations are sample grinding, impurity collector, reagents, intermediate operations, auxiliary materials, and laboratory air. There are ways of decreasing the degree of contamination. The potential of spectrochemical determination can be almost completely accomplished by rationally performed impurity preconcentration. We developed variatrons of the preconcentration of impurities by matrix elimination exemplified by the determination of impurities in high-purity silicon, germanium, and their oxides; arsenic, arsenic sulfides, selenium, tellurium, zirconium tetrafluoride, xenon difluoride, and chalcogenide glasses by atomic emission and atomic absorption spectrometry. Acids and high-purity water with concentrations of metal impurities of no higher than 0.1–0.001 ppb were used throughout. Test samples were purified from impurities in a class-100 clean room. To transfer germanium, silicon, their oxides, arsenic sulfides, and matrices of chalcogenide glasses to volatile compounds, we used the headspace autoclave dissolution of gram-level weighed portions by acids or xenon difluoride. Arsenic, arsenic monosulfide, selenium, and tellurium were eliminated under normal pressure in air; zirconium tetrafluoride was eliminated in a flow of purified helium; and silicon tetrafluoride under a lowered pressure and temperature.