A method for producing a deep-nested embossed product is disclosed. The method comprises the steps of: a) providing an embossing apparatus having mating first and second embossing members; b) providing the first embossing member with a plurality of discrete embossing elements in a non-random pattern; c) providing the second embossing member with at least one linear embossing element; d) coordinating the at least one linear embossing element with the non-random pattern of first embossing elements; e) aligning the first embossing member and the second embossing member so that the non-random pattern of first embossing elements nest with the at least one linear embossing element to an engagement depth of greater than about 0.01 mm; f) providing one or more plies of material to the embossing apparatus; and, g) passing the one or more plies of the material between the first and second embossing members to produce the deep-nested embossed product.