A forming fabric for a papermaking machine has a machine facing side and a web facing side. The web facing side has a structured weave of warp yarns and weft yarns that define pockets on the web facing side. Each pocket is defined by four sides on the web facing side, three of the four sides each being formed by a knuckle of a single yarn, and one of the sides being formed by a knuckle of a weft and of a warp yarn, wherein the weft yarn also defines a bottom surface of the pocket.