An embossing apparatus and method which provides a better embossed appearance and eliminates undesired roughness on the backside of the web material. Two plies are multilevel embossed between rigid engraved rolls and backup rolls, which may be either engraved or smooth. One rigid roll has embossing elements of varying heights and perforation elements, which run in a side-by-side relationship with the corresponding perforation elements on the opposing rigid roll in a nip region of the apparatus. The multiple plies are perforation bonded between the perforation elements, which are preferably the two highest elements, thus reinforcing the other multi-level embossed pattern formed in between the perforation bonds. The embossed patterns impart a quilt-like contoured appearance to the finished product.