A woven fabric for use in a machine to produce a fiber web, such as a tissue fiber web. A paper side of the fabric has warp yarns and weft yarns interwoven in a weave pattern, and twill lines, each formed by neighboring warp yarn flotations. Each warp yarn flotation of the weave pattern that contributes to the formation of the twill lines passes over a first weft yarn, which passes over a first warp yarn that directly neighbors the warp yarn flotation on a first side and passes below a second warp yarn that directly neighbors the warp yarn flotation on a second side opposite the first side. The warp yarn flotation also passes over a second weft yarn that directly neighbors the first weft yarn, and the second weft yarn passes below the first warp yarn and over the second warp yarn.