A process for producing polysilicon, includes a) depositing polycrystalline silicon on filaments using reaction gas containing silicon-containing component (SCC) containing trichlorosilane, and hydrogen, wherein molar saturation of SCC based on hydrogen is at least 25%; b) feeding offgas from the deposition into a cooling apparatus, i) wherein condensed offgas components containing SiCl4 are conducted to an apparatus which enables distillative purification of the condensate, and ii) non-condensing components are conducted to an adsorption or desorption unit; c) obtaining a first stream of non-condensing components purified by adsorption and containing hydrogen; and d) obtaining, during adsorption unit regeneration, a second stream of non-condensing components, containing SiCl4 which is then preferably supplied to a converter for conversion of SiCl4 to trichlorosilane. A process for depositing polysilicon on filaments with a reaction gas includes a SCC and hydrogen, wherein molar saturation of SCC based on hydrogen is at least 25%.