There is provided a process for treating a process gas or liquid to remove acid gases which includes treating a relatively lean amine gas scrubbing solution to further reduce the acid gas content of at least a portion of that lean amine gas scrubbing solution such that it becomes an ultra-lean amine solution (one substantially free of acid gas) and the beneficial use of the ultra-lean amine solution to obtain further reductions in the acid gas contents of specific gas or liquid process streams not possible with lean amine solutions having higher residual acid gas loadings. In another aspect of this invention, there is provided a process for producing the ultra-lean amine.