Carbon dioxide and other acid gases are removed from gaseous streams using aqueous absorption and stripping processes. By replacing the conventional stripper used to regenerate the aqueous solvent and capture the acid gas with a matrix stripping configuration, less energy is consumed. The matrix stripping configuration uses two or more reboiled strippers at different pressures. The rich feed from the absorption equipment is split among the strippers, and partially regenerated solvent from the highest pressure stripper flows to the middle of sequentially lower pressure strippers in a “matrix” pattern. By selecting certain parameters of the matrix stripping configuration such that the total energy required by the strippers to achieve a desired percentage of acid gas removal from the gaseous stream is minimized, further energy savings can be realized.