An absorbent cellulosic sheet having variable local basis weight includes a papermaking-fiber reticulum provided with (i) a plurality of cross-machine direction (CD) extending, fiber-enriched pileated regions of relatively high local basis weight interconnected by (ii) a plurality of elongated densified regions of compressed papermaking fibers. The elongated densified regions have relatively low local basis weight and are generally oriented along the machine direction (MD) of the sheet and have an MD/CD aspect ratio of at least 1.5. The products are most preferably prepared by way of a compactive dewatering/wet crepe process.