The present invention is directed to multiple-layer composites suitable for use as floor-coverings in the form of cut tiles or broadloom sheets, providing a durable and highly stable structure that can lay flat and remain flat with variations in temperature and humidity and provide a durable and yet soft textile face. The composite comprises a laterally-compressible fabric face bonded with an adhesive layer to a highly conformable stress-absorbing cushioning layer. The face fabric comprises closely packed looped yarns reciprocating between the top and the bottom of the fabric, protruding into the adhesive layer and emerging from the adhesive layer to the surface forming micro-spring structures. The weight, properties, density and level of penetration of adhesive are controlled to maintain lateral compressibility for the entire composite and avoid warping.