A process for making absorbent towel paper webs is provided. The process has the steps of (a) providing a papermaking furnish having from about 45% to about 90% by weight of the dry fiber basis of the absorbent towel paper web of a refined softwood pulp fiber mixture having from about 20% to about 89.9% by weight of softwood pulp fiber, from about 0.05% to about 20% by weight of cellulose nanofilaments, and from about 0.05% to about 5.0% by weight of strengthening additive, and from about 10% to about 55% by weight of the dry fiber basis of the absorbent towel paper web of a hardwood pulp fiber mixture; (b) forming a wet fibrous web from the paper making furnish; and, (c) drying the web until the web contains not more than about 10% by weight moisture.