A method for recovering methane gas from a landfill involves the use of a main absorber, a flash system, an ancillary absorber and a polishing absorber. The main absorber uses a main current of solvent for absorbing most of the carbon dioxide from raw landfill gas. The flash system removes much of the carbon dioxide from the solvent exiting the main absorber. A portion of the solvent downstream of the flash system is diverted to the ancillary absorber in which a current of air removes additional carbon dioxide from that portion of solvent. From the ancillary absorber, the diverted portion of solvent flows through the polishing absorber to remove additional carbon dioxide from the main current of solvent that was previously treated in the main absorber. To increase the energy content of the processed gas, in some examples, propane is added to the final outgoing gas stream.