A method of making an embossed air-laid absorbent sheet includes: depositing a dry web of fibers on a foraminous support; embossing the compacted web with a laser engraved roll provided with a hard rubber embossing surface having an embossing pattern with a depth of from about 5 mils to about 100 mils. The hard rubber embossing surface is biased toward a second embossing surface selected from the group consisting of the surface of a nip roll and a foraminous web support engaging a support embossing roll. The process further includes bonding the web.