A woven wire for use in a paper, cardboard, or tissue manufacturing machine, has a first fabric layer providing a web-contact side and a second fabric layer providing a machine-contact side. The layers have machine-direction threads, cross-direction threads, and binder threads. A first fabric layer has a weaving pattern of interwoven first MD threads, first CD threads and binder threads. The second fabric layer has a weaving pattern of interwoven second MD threads and second CD threads. The first and second fabric layers are interconnected by binder threads. The binder threads are interwoven with MD threads and/or CD threads of the first and of the second fabric layers. The first MD threads, the first CD threads and the binder threads have a circular cross-sectional face. At least some or all second MD threads have a cross-sectional face with a flattened shape different from a circular shape.