Fiber-containing composites are described that contain woven or non-woven fibers, and a cured binder formed from a binder composition that includes (1) a reducing sugar and (2) a crosslinking agent that includes a reaction product of a urea compound and a polycarbonyl compound. Exemplary reaction products for the crosslinking agent may include the reaction product of urea and an α,β-bicarbonyl compound or an α,γ-bicarbonyl compound. Exemplary fiber-containing composites may include fiberglass insulation.