A solvent for absorbing H2S and CO2 is regenerated using two regenerators. Rich solvent is fed to a first regenerator producing a first acid gas stream from the top, and a partially regenerated solvent from the bottom. The partially regenerated solvent is fed to a second regenerator producing an overhead vapor stream from the top and a lean solvent stream from the bottom. A portion of the second regenerator overhead vapor stream is cascaded to the first regenerator to contact rich solvent. The first acid gas stream and the remaining second regenerator overhead vapor stream are respectively fed to the first and second reaction zones of a two-stage Claus reaction furnace. Substantially all volatile organic contaminants are stripped in the first regenerator, and thus favorably destroyed in the first reaction furnace zone by virtue of higher local combustion temperatures and closer approach to oxidizing conditions.