Topically-applied binder materials for imparting wet strength to soft, absorbent paper sheets, such as are useful as household paper towels and the like, include an azetidinium-reactive polymer, such as a carboxyl-functional polymer, an azetidinium-functional polymer and, optionally, a component useful for reducing sheet-to-sheet adhesion (blocking) in the product. These binder materials can be cured at ambient temperature over a period of days and do not impart objectionable odor to final product when wetted.