A refined Karman-Pohlhausen method previously generalized by Zien to include the effects of mass transfer is further explored and its application is extended to cases involving both pressure gradients and surface mass transfer. The case with piece-wise suction (or blowing) is also included. The study is restricted to plane, incompressible, laminar boundary layers. Configurations of flat plates and circular cylinders are chosen to illustrate the application of the method. Results are given mainly in terms of skin frictions, and they are presented entirely in closed forms. The calculations for the porous plate case are carried out using rather elaborate velocity profiles, but the results differ negligibly from previous ones with very simple profiles. A linear velocity profile is then used to carry out some exploratory calculations for more complex flows. The method is shown to be a potentially efficient tool for handling the problem of boundary-layer control by means of surface mass transfer. (Author).