The present invention provides a unique knit construction having a nonfiberglass stiffness-controlling yarn in the fabric of the backing. Preferably, the nonfiberglass stiffness-controlling yarn is used in combination with a heat shrinkable yarn or a stretch yarn, and alternatively a nonfiberglass microdenier yarn. More preferably, the nonfiberglass stiffness-controlling yarn is in combination with a stretch yarn and a nonfiberglass microdenier yarn. Most preferably, the nonfiberglass stiffness-controlling yarn is in combination with a heat shrinkable, elastically extensible yarn, and a nonfiberglass microdenier yarn.