Abstract: A papermaking fabric having a top layer and a bottom layer of interwoven machine direction (MD) yarns and cross-machine direction (CD) yarns bound together with warp binder yarns. At least some of the CD yarns are made of a material which generates a strong contractive force when returned to room temperature after heat-setting (annealing under MD tension). These CD yarns are positioned such that the strong contractive force offsets tension forces generated when the fabric is placed under load and which typically result in an edge curl. An exemplary material for these CD yarns is polybutylene terephthalate (PBT).