An improved curable formaldehyde-free binding composition is provided. Such curable composition comprises the reaction product of a polyanhydride and a polyol crosslinker and a lower molecular weight anhydride. Initially, the polyanhydride is modified through reaction with a polyol (e.g., a glycol or an alkanolamine) and subsequently is grafted with the lower molecular weight anhydride (e.g., maleic anhydride) to form a water-soluble or water-dispersible curable reaction product. The composition is well suited for binding fibrous materials (e.g., a mat of glass fibers) or for bonding together non-fibrous materials. The binder composition displays an advantageous viscosity so as to facilitate a flowable application with ease combined with an adequately high molecular weight to satisfactorily undergo service as a binder following curing even when harsh environmental conditions (e.g., hot humid air) are encountered for a prolonged period of time.