The present invention relates to processes for producing a deep-nested embossed paper products. The invention relates to a process for producing a deep-nested embossed paper products comprising one or more plies of paper where the resulting embossed ply or plies of paper comprise a plurality of embossments having an average embossment height of at least about 650 μm and have a high finished product wet burst strength relative to the unembossed wet strength. The present invention relates to a process for producing deep-nested embossed paper products comprising the steps of a) delivering one or more plies of paper to a deep-nested embossing process, b) conditioning the one or more plies of paper, wherein the conditioning step comprises heating the one or more plies of paper, adding moisture to the one or more plies of paper, or both heating and adding moisture to the one or more plies of paper, and c) embossing the one or more plies of the paper where the resulting embossed ply or plies of paper comprise a plurality of embossments having an average embossment height of at least about 650 μm.