A method of achieving at least 99.7% sulfur recovery from an acid gas stream having a hydrogen sulfide concentration of 20% or less and having a carbon dioxide concentration of 80% or more for increasing the concentration of hydrogen sulfide in a gas stream, comprising: separating the acid gas stream in a first absorber to form a first carbon dioxide enriched overhead and a first-hydrogen sulfide enriched solvent using a first portion of a lean hydrogen sulfide selective solvent (10, 19, 20, 21), a first portion of a second hydrogen sulfide enriched solvent (34, 35), and a first portion of a hydrogen sulfide rich stream obtained from a hydrogen sulfide rich product gas; wherein the first portion of the lean hydrogen sulfide selective solvent (10, 19, 20, 21) is fed to the top of the first absorber, wherein the acid gas stream is fed to a section between a mid section and a bottom of the first absorber, wherein the first portion of the second hydrogen sulfide enriched solvent (34, 35) is fed to the mid section of the first absorber, and wherein the first portion of the hydrogen sulfide rich stream is fed to the bottom of the first absorber; combining the first hydrogen sulfide enriched solvent (4, 7) from the first absorber and a second portion of the second hydrogen sulfide enriched solvent (34, 35) to form a combined hydrogen sulfide enriched solvent (36, 8); removing hydrogen sulfide from the combined hydrogen sulfide enriched solvent (36, 8) in a regenerator to thereby form the hydrogen sulfide rich product gas and the lean hydrogen sulfide selective solvent (10, 19, 20, 21); feeding a second portion of the hydrogen sulfide rich stream to a Claus plant to thereby produce a Claus unit effluent gas, and feeding the Claus unit effluent gas to a hydrogenation unit to thereby produce a hydrogenated gas; and separating the hydrogenated gas in a third absorber using a second portion of the lean hydrogen sulfide selective solvent (10, 19, 20, 21) to thereby form a second carbon dioxide enriched overhead and the second hydrogen sulfide enriched solvent; and combining the second carbon dioxide enriched overhead and the first carbon dioxide enriched overhead. separating the acid gas stream in a first absorber to form a first carbon dioxide enriched overhead and a first-hydrogen sulfide enriched solvent using a first portion of a lean hydrogen sulfide selective solvent (10, 19, 20, 21), a first portion of a second hydrogen sulfide enriched solvent (34, 35), and a first portion of a hydrogen sulfide rich stream obtained from a hydrogen sulfide rich product gas; wherein the first portion of the lean hydrogen sulfide selective solvent (10, 19, 20, 21) is fed to the top of the first absorber, wherein the acid gas stream is fed to a section between a mid section and a bottom of the first absorber, wherein the first portion of the second hydrogen sulfide enriched solvent (34, 35) is fed to the mid section of the first absorber, and wherein the first portion of the hydrogen sulfide rich stream is fed to the bottom of the first absorber; combining the first hydrogen sulfide enriched solvent (4, 7) from the first absorber and a second portion of the second hydrogen sulfide enriched solvent (34, 35) to form a combined hydrogen sulfide enriched solvent (36, 8); removing hydrogen sulfide from the combined hydrogen sulfide enriched solvent (36, 8) in a regenerator to thereby form the hydrogen sulfide rich product gas and the lean hydrogen sulfide selective solvent (10, 19, 20, 21); feeding a second portion of the hydrogen sulfide rich stream to a Claus plant to thereby produce a Claus unit effluent gas, and feeding the Claus unit effluent gas to a hydrogenation unit to thereby produce a hydrogenated gas; and separating the hydrogenated gas in a third absorber using a second portion of the lean hydrogen sulfide selective solvent (10, 19, 20, 21) to thereby form a second carbon dioxide enriched overhead and the second hydrogen sulfide enriched solvent; and combining the second carbon dioxide enriched overhead and the first carbon dioxide enriched overhead.