A low-compaction method of making an absorbent cellulosic web includes: forming a nascent web from a papermaking furnish; dewatering the nascent web to a consistency of from about 10 to about 30 percent on a foraminous forming support traveling at a first speed; rush-transferring the web at a consistency of from 10 to about 30 percent to an open texture fabric traveling at a second speed slower than the first speed of the forming support; further dewatering the web on the impression fabric to a consistency of from about 30 to about 60 percent by way of (i) combining the open texture fabric bearing said web with a fluid distribution membrane and an anti-rewet felt as the three pass through a nip into a pressure chamber defined in part by a plurality of nip rolls, the fluid distribution membrane bearing against the side of the open texture fabric away from the web, with the anti-rewet felt bearing against the web, and (ii) applying a pneumatic pressure gradient from the distributor membrane through the web thereby dewatering the web; and drying the web. Preferably the process includes the steps of selecting the papermaking furnish and controlling the process such that the dried web has a void volume fraction of at least 0.7, a hydraulic diameter in the range of from about 3 to about 20 microns and a Wet Springback Ratio of at least about 0.65. Optionally provided is a high solids fabric crepe in a pressure nip.