A dispersible wet wipe includes a layer of cellulosic fibers. In one embodiment, a first binder is applied in a coating comprising randomly distributed deposits of the binder. A second binder is applied in an intermittent pattern on the surface to define first regions on the surface that include first binder but no second binder and to define second regions on the surface that include both first binder and second binder. The first and second binders can have the same chemical composition. In a second embodiment, a first binder is applied to a web surface in a first pattern, and, after applying the first binder, a second binder is applied to the web surface in a second pattern that is different than the first pattern. In a third embodiment, a binder is applied to a web surface in a pattern, the pattern having first regions and second regions, wherein the add-on level of the binder in the first regions is lower than the add-on level of the binder in the second regions.