The present invention relates to an apparatus for producing a deep-nested embossed paper product comprising two embossing cylinders, each cylinder having a plurality of protrusions on its surface. The protrusions on each cylinder are disposed in a non-random pattern where the respective non-random patterns are coordinated to each other. The two embossing cylinders are aligned such that the respective coordinated non-random pattern of protrusions nest together such that the protrusions engage each other to a depth of greater than about 1.016 mm. The protrusions each comprise a top plane and sidewalls, with the top plane and sidewalls meeting at a protrusion corner. The protrusion corners of the protrusions of the embossing cylinders of the apparatus of the present invention have a radius of curvature ranging from about 0.076 mm to about 1.778 mm.