Formaldehyde-free binder compositions are described that include an aldehyde or ketone, a reaction product between a polyamine and an organic anhydride, and an acidic compound. The acidic compound may be an organic acid, an acidic catalyst, or both. The acidic compound is supplied in quantities that lower the pH of the binder composition to about 5 or less. The binder compositions may be used in methods of binding fiberglass and the resulting fiberglass products have an improved tensile strength due to the addition of the acidic compound.