A woven papermaker fabric having a first woven fabric layer made of first threads and having a second woven fabric layer made of second threads, the two woven fabric layers being connected by binder threads formed by structural second threads at binder points and having knuckles having peaks constituting a peak plane parallel to a paper side plane, and the first threads forming knuckles with concave inner bends, the points of which lying nearest to the paper side plane constituting an inner plane, wherein the tension of the first threads extending transversely to the binder threads is such that the peak plane is nearer to the paper side plane than the inner plane thereby causing lateral deflections of at least one of the first threads.