A limiting orifice through-air-drying medium for papermaking or other absorbent embryonic webs. The medium may be used in an apparatus which can be embodied in a cover and a roll. The medium has the unique combination of a relatively high bending fatigue strength and relatively low pressure drop. The medium may comprise a laminate of a plurality of plies. The intermediate plies of the laminate may be woven with a square weave. The medium may also be used for other types of drying.