The present invention provides a wet pressed paper web. The web has a first relatively high density region having a first thickness K, a second relatively low density region having a second thickness P, which is a local maxima, and a third region extending intermediate the first and second regions. The third region includes a transition region having a third thickness T, which is a local minima. The present invention also provides a method of making a wet pressed web. An embryonic web of papermaking fibers is formed on a foraminous forming member, and transferred to an imprinting member to deflect a portion of the papermaking fibers in the embryonic web into deflection conduits in the imprinting member. The web and the imprinting member are then pressed between first and second dewatering felts in a compression nip to further deflect the papermaking fibers into the deflection conduits in the imprinting member and to remove water from both sides of the web. The imprinting member can have a continuous, monoplanar web contacting surface for molding a wet paper web to have a continuous, relatively high density network and a plurality of relatively low density, discrete domes dispersed through the relatively high density network.