An apparatus for producing a deep-nested embossed product including a first embossing member and a second embossing member. The first embossing member has a plurality of discrete embossing elements disposed in a first non-random pattern. The second embossing member has a plurality of second embossing elements including at least one linear embossing element. The second embossing elements are disposed in a second non-random pattern such the first non-random pattern and the second non-random pattern nest together to a depth of greater than about 0.01 mm.