A method for producing a flushable hydroentangled moist wipe or hygiene tissue includes the steps of: dry-, wet-, or foam-forming a fibrous web on a moving support, hydroentangling said fibrous web in a hydroentangling station to form a hydroentangled nonwoven web. The moving support includes a plurality of protruding elongated elements protruding above the surface of the moving support. The protruding elements will produce weakenings in the hydroentangled web.