A method of separating impurities from a natural gas stream. The natural gas stream is cooled through heat exchange with one or more process streams to produce a chilled gas stream, which is contacted with a lean solvent stream in a contactor to separate hydrogen sulfide (H2S) from the chilled gas stream, thereby producing a rich solvent stream and a partially-treated gas stream. Carbon dioxide (CO2) and H2S are separated from the partially-treated gas stream in a membrane separation system, thereby creating a fully-treated gas stream and a permeate gas stream, the permeate gas stream being comprised primarily of H2S and CO2, and the fully-treated gas stream being comprised primarily of natural gas. The fully-treated gas stream and the permeate gas stream are at a lower temperature than the partially-treated gas stream. The fully-treated gas stream and the permeate gas stream comprise the one or more process streams.