Hollow fiber membranes were prepared from TEGMC (TriEthylene Glycol Monoesterified Crosslinkable) 6FDA-DAM: DABA (3:2) polyimide and shown to retain their stability and permselectivity under aggressive sour gas feed conditions. The H2S/CH4 and CO2/CH4 permselectivities of these cross-linked fibers exceeded those of dense-film membranes, which is attributed to polymer-chain alignment induced during the spinning process. Morover, when the crosslinked fibers were post-treated to deposit a polydimethylsiloxane (PDMS) layer on the skin, high-pressure performance under mixed-gas feeds improved even further. We hypothesize that the PDMS layer healed subtle morphological imperfections in the chain-oriented fiber skin even under challenging feed conditions. The high-performance membranes showed CO2/CH4 and H2S/CH4 permselectivity values as high as 55 and 29, respectively for a 5% H2S, 45% CO2, and 50% CH4 feed at 35 degrees C. An even more aggressive 20% H2S, 20% CO2, 60% CH4 mixed gas feed with 500 psig feed pressure was also used and showed CO2/CH4 and H2S/CH4 permselectivity values of 47 and 22, respectively.