A pocketed spring assembly comprises a plurality of parallel strings of individually pocketed springs. Each string is joined to at least one adjacent string. Each string has first and second opposed plies of fabric and a plurality of pockets formed along a length of the string by transverse seams joining the plies. At least one spring is positioned in each of the pockets. The double-layered fabric used to make at least some strings comprises two layers of non-woven spunbonded polypropylene fabric to reduce noise. The layers may be ultrasonically welded or point bonded together.