A method for Kraft pulping employing a modified cooking process in conjunction with polysulfide pulping technologies to obtain higher pulping yields than obtained in the prior art. The total required alkali charge (polysulfide liquor) is added to the beginning of a cook, and after all polysulfide has essentially reacted with lignocellulosic material at temperature below that at which no significant carbohydrate degradation occurs, a first quantity of the cooking liquor high in effective alkali (EA) concentration is removed from a first point in the pulping process and replaced with a cooking liquor low in EA concentration removed from another process point. The first quantity is then added elsewhere in the pulping process, where the EA concentration is low. This cooking liquor “exchange” obtains the full yield benefit from polysulfide pulping and a more uniform EA concentration profile to retain the major benefits of modified cooking.