Processes for making absorbent towel paper and soft sanitary tissue paper webs are provided. The processes provide the steps of: (a) providing a papermaking furnish, (b) forming a wet fibrous web having a differential density from the paper making furnish; and, (c) drying the differential density wet fibrous web to not more than about 10% by weight moisture. Step a) provides: i) from about 20.1% to about 99.9% by weight of a softwood pulp fiber mixture; and, ii) from greater than 0% to about 79.9% by weight of a hardwood pulp fiber mixture. Step i) provides u) from about 20.0% to about 99.8% by weight of softwood pulp fiber; and, v) from about 0.05% to about 5.0% by weight of strengthening additive. Step ii) provides w) from about 0.05% to about 79.4% by weight of hardwood pulp fibers; and, x) from about 0.05% to about 20.0% by weight of cellulose nano-filaments.