Tissue paper webs useful in the manufacture of soft, absorbent products such as paper towels, napkins, and facial tissues, and processes for making the webs. The tissue paper webs comprise papermaking fibers, a biodegradable quaternized amine-ester softening compound, a wetting agent, and a permanent wet strength resin. The process comprises a first step of forming an aqueous papermaking furnish from the above-mentioned components. The second and third steps in the basic process are the deposition of the papermaking furnish onto a foraminous surface such as a Fourdrinier wire and removal of the water from the deposited furnish. An alternate process involves the use of the furnish containing the aforementioned components in a papermaking process which will produce a pattern densified fibrous web having a relatively high bulk field of relatively low fiber density in a patterned array of spaced zones of relatively high fiber density.