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 first carbon moiety selected from an aldehyde, a ketone, a nitrile, and a nitro group, wherein an α-carbon atom having at least one acidic hydrogen is directly bonded to the first carbon moiety. Exemplary reducing sugars include dextrose and exemplary crosslinking agents include glyoxal. Exemplary fiber-containing composites may include fiberglass insulation.