Abstract: A tapered tubular polyester sleeve as set forth. It has a large end 12 and a small end 14 with a length to be determined. The ratio of taper is also determined by scale factors. All the warp yarns extend to the large end 12. A requisite number of warp yarns 16 extend the full length of the sleeve. Other warp yarns exemplified at 18, 22, 26, 28, 30 and 32 extend from the large end but are terminated along the length of the sleeve. It is then woven with a filling yarn 40 which extends in a full circle along the full length of the sleeve to thereby define the tapered sleeve. The sleeve after fabrication is then placed on a mandrel 42, heated in an oven 44 and is thereafter placed on the arm or other limb of a space suit exemplified at 50.