A process for selectively separating H2S from a gas mixture which also comprises CO2 is disclosed. A stream of the gas mixture is contacted with an absorbent solution comprising one or more amines, alkanolamines, hindered alkanolamines, capped alkanolamines, or mixtures thereof. The H2S/CO2 selectivity of the absorbent solution is preferably greater than about 4.0 for an acid gas loading [mol(CO2+H2S)/mol(amine)] between about 0.2 and about 0.6, and is achieved by reducing pH of the absorbent solution.