A method and apparatus for recovering a gaseous component from an incoming gas stream is described. The incoming gas stream is contacted with a lean aqueous absorbing medium to absorb at least a portion of the gaseous component from the incoming gas stream to form a lean treated gas stream and a rich aqueous absorbing medium. At least a portion of the gaseous component is desorbed from the rich aqueous absorbing medium at a temperature to form an overhead gas stream and a regenerated aqueous absorbing medium. At least a portion of the overhead gas stream is treated to recover a condensate stream. At least a portion of the condensate stream is used to form a heated stream. At least a portion of the heated stream is recycled back to the desorbing step. Novel absorbing medium compositions to recover carbon dioxide and/or hydrogen sulfide are also described.