A wet wipe contains fibrous material, a binder composition for binding the fibrous material into an integral web, and a wetting composition containing water, a salt, and at least about 10 wt % of an organic solvent. The binder composition contains an ionic copolymer. The wet wipe is not dispersible in the wetting composition, and is dispersible in water containing up to 200 ppm of one or more multivalent ions. The ionic copolymer may be the polymerization product of a vinyl-functional cationic monomer and at least one non-ionic vinyl monomer. The ionic copolymer may be the polymerization product of a vinyl-functional anionic monomer and at least one non-ionic vinyl monomer.