A process for the removal of hydrogen sulfide from a gas stream in which the gas stream is first passed through a Claus unit operating at a sub-stoichiometric ratio (H2S:SO2) of greater than 2:1 to produce a tail gas stream comprising less than 2000 vppm SO2. This tail gas stream is then treated to increase the sulfur recovery to at least 99.5% by first directly cooling the tail gas stream by contact with water as a coolant, followed by contacting the gas stream with a circulating stream of a dilute, absorbent solution of a severely sterically hindered secondary aminoether alcohol to further cool the gas stream, and then removing the H2S from the stream using a stronger absorbent solution of a severely sterically hindered secondary aminoether alcohol.