An exemplary embodiment can be a process for sweetening natural gas to liquefied natural gas specifications. The process can include providing a membrane contactor having a lumen side and a shell side. A feed natural gas is introduced to the lumen side of the membrane contactor. An absorption solvent is introduced to the shell side of the membrane contactor. CO2 and H2S are removed with the absorption solvent from the feed natural gas resulting in a sweetened natural gas containing less than 50 ppmv CO2 and less than 4 ppmv H2S. Corresponding or associated systems for such sweetening of natural gas are also provided.