The invention relates to a process for separating a component mixture (K) comprising hydrogen, methane, hydrocarbons having two carbon atoms and hydrocarbons having three or more carbon atoms, wherein in a deethanization at least a portion of the component mixture (K) is subjected to a first partial condensation by cooling from a first temperature level to a second temperature level at a first pressure level to obtain a first gas fraction (G1) and a first liquid fraction (C1), at least a portion of the first gas fraction (G1) is subjected to a second partial condensation by cooling from the second temperature level to a third temperature level at the first pressure level to obtain a second gas fraction (G4) and a second liquid fraction (C2), and at least a portion of the first liquid fraction (C1) and at least a portion of the second liquid fraction (C2) are subjected to a rectification to obtain a third gas fraction (G3) and a third liquid fraction (C3+). The first liquid fraction (C1) or its part subjected to the rectification and the second liquid fraction (C2) or its part subjected to the rectification are expanded to a second pressure level and the rectification is carried out at the second pressure level, the first pressure level being 25 to 35 bar and the second pressure level being 14 to 17 bar. An overhead gas formed during the rectification is cooled to −25 to −35° C. and partially condensed, wherein a condensed portion of the overhead gas is used partially or completely as a reflux in the rectification and an uncondensed portion of the overhead gas is provided partially or completely as the third gas fraction (G3). The present invention likewise provides a corresponding plant (100, 200).