Methods and apparatuses for enhancing absorption of acid gas components from sour feed gas are provided. In an embodiment, a method for processing a gas includes contacting a feed gas stream which comprises hydrocarbon and hydrogen sulfide and carbon dioxide with a liquid absorbent in a multistage counterflow absorption zone to absorb hydrogen sulfide and carbon dioxide from the feed gas stream into the liquid absorbent. The method produces an effluent liquid stream rich in hydrogen sulfide and carbon dioxide and a treated gas stream. Further, the method includes removing a portion of the liquid absorbent from an interstage location in the multistage counterflow absorption zone. The portion of the liquid absorbent is cooled to form a cooled portion, and the cooled portion is returned to the interstage location.