An aircraft or spacecraft gas compression system, comprising: a system inlet (140, 220, 240, 260) configured to receive a gas stream containing a first component and a second component; a vapor system outlet (150, 222, 242, 262) configured to discharge the gas stream; and a plurality of compression stages (142a, 142b) coupled in series between the system inlet (140, 220, 240, 260) and the vapor system outlet (150, 222, 242, 262), wherein each subsequent compression stage has a smaller volumetric capacity than a preceding compression stage, and wherein each of the plurality of compression stages (142a, 142b) comprises: a compressor (144a, 144b, 254) configured to receive the gas stream from either the system inlet (140, 220, 240, 260) or another of the plurality of compression stages (142a, 142b) and compress the gas stream; a condenser (146a, 146b) coupled to the compressor (144a, 144b, 254), the condenser (146a, 146b) configured to condense the second component from the gas stream; and a gravity-independent phase separator (148a, 148b) coupled to the condenser (146a, 146b), the gravity-independent phase separator (148a, 148b) configured to remove the second component from the gas stream and discharge the gas stream to either the vapor system outlet (150, 222, 242, 262) or another of the plurality of compression stages (142a, 142b). a system inlet (140, 220, 240, 260) configured to receive a gas stream containing a first component and a second component; a vapor system outlet (150, 222, 242, 262) configured to discharge the gas stream; and a plurality of compression stages (142a, 142b) coupled in series between the system inlet (140, 220, 240, 260) and the vapor system outlet (150, 222, 242, 262), wherein each subsequent compression stage has a smaller volumetric capacity than a preceding compression stage, and wherein each of the plurality of compression stages (142a, 142b) comprises: a compressor (144a, 144b, 254) configured to receive the gas stream from either the system inlet (140, 220, 240, 260) or another of the plurality of compression stages (142a, 142b) and compress the gas stream; a condenser (146a, 146b) coupled to the compressor (144a, 144b, 254), the condenser (146a, 146b) configured to condense the second component from the gas stream; and a gravity-independent phase separator (148a, 148b) coupled to the condenser (146a, 146b), the gravity-independent phase separator (148a, 148b) configured to remove the second component from the gas stream and discharge the gas stream to either the vapor system outlet (150, 222, 242, 262) or another of the plurality of compression stages (142a, 142b). a compressor (144a, 144b, 254) configured to receive the gas stream from either the system inlet (140, 220, 240, 260) or another of the plurality of compression stages (142a, 142b) and compress the gas stream; a condenser (146a, 146b) coupled to the compressor (144a, 144b, 254), the condenser (146a, 146b) configured to condense the second component from the gas stream; and a gravity-independent phase separator (148a, 148b) coupled to the condenser (146a, 146b), the gravity-independent phase separator (148a, 148b) configured to remove the second component from the gas stream and discharge the gas stream to either the vapor system outlet (150, 222, 242, 262) or another of the plurality of compression stages (142a, 142b).