A woven paper making fabric (A) is disclosed having a profiled permeability characteristic which varies across the width of the fabric yet the tensions are relatively uniform across the width of the fabric. The fabric includes a plurality of warp yarns (20, 22, 24, 26) extending in a machine direction and a plurality of weft yarns (28, 30, 32) extending in a cross-machine direction in the fabric woven with the warp yarns. The weft yarns and warp yarns are woven to provide at least two layers (60, 62, 64) in the fabric. A number of unwoven fabric closure elements (B) are bound between the weft yarns of two of the fabric layers (60, 62) extending in the machine direction adjacent the lateral edges (42, 44) of the fabric (A). The closure elements (B) extend through the fabric parallel to the edges in a generally straight configuration between the two fabric layers (60, 62) in a generally tensionless state so as not to effect the tension of the weave of the fabric. A uniform weave tension exists across the width of said fabric. The closure elements block the flow of air through the fabric to reduce the permeability of the fabric at the lateral edges (46, 48) and provide the desired permeability profile.