An improved process is described for reducing the total sulfur content of off-gases from a Claus process by catalytically converting the sulfur compounds contained in the off-gases to hydrogen sulfide and selectively absorbing the hydrogen sulfide with a regenerable polyalkanolamine adsorbent solution; the hydrogen sulfide enriched adsorbent being regenerated and used again for further adsorption of hydrogen sulfide and the hydrogen sulfide-rich gas mixture liberated in regeneration being passed to a Claus process. This improved process is characterized in that the hydrogen sulfide enriched polyalkanolamine solution from adsorption of the reduced Claus off-gases is further enriched in hydrogen sulfide content prior to regeneration by contacting it with a stream which contains hydrogen sulfide at a higher partial pressure than that of the reduced Claus off-gases. 6 claims, 1 drawing figure.