A tubular woven implantable graft having a tapered section is provided. The graft comprises a first diameter and a second diameter and has a generally constant number of warp yarns per inch adjacent both the first diameter and the second diameter. A method for producing an implantable woven graft is also provided. The method includes weaving a first section having a first diameter and a tapered diameter tapering from the first diameter to a second diameter. During weaving of the tapered section a number of warp yarns are dropped from the weave and compressive forces are applied to the fabric to narrow the width of the fabric.