A dispersible fibrous structure having an in-use wet tensile strength of at least about 40 g/cm; a disposable wet tensile decay of at least about 35% and a method of making the structure. The structure has at least one property selected from a group consisting of: a wet CD maximum slope of less than about 12 kg/7.62 cm, a wet CD Elongation of greater than about 50%, a low elongation CD modulus of less than about 5.0 kg/7.62 cm, and a wet CD Bending of less than about 0.05 gf cm/cm.