A soft, absorbent nonwoven fibrous web, such as a wet wipe, capable of dispersing in an aqueous environment into unrecognizable pieces, made by a method comprising the steps of forming a wet-laid nonwoven web from an aqueous slurry of fibers; hydraulically needling the wet-laid nonwoven web; partially drying the hydraulically needled web; applying a binder composition to one side of the web; creping the web such that interfiber adhesion is disrupted and z-direction fiber orientation is introduced; optionally applying a binder composition to the second side of the web; recreping the web; drying and curing the web; and, converting the dried and cured web into a wet wipe, dry wipe, or other absorbent article. In the case of a wet wipe, a solution containing about 100 ppm of calcium ion is applied to the web, such as in a preserving solution. In the case of a dry wipe, the calcium ion is added after the binder is added to the web, and the final product is stored in a dry state. The combination of processes produces a web having desirable tensile strength, bulk and softness during storage and use, yet will disperse in an aqueous environment into unrecognizable pieces.