The inverse-amplitude method is applied to the one-loop chiral expansion of the pion, kaon, and K l3 form factors. Since these form factors are determined by the same chiral low-energy constants, it is possible to obtain finite predictions for the inverse-amplitude method. It is shown that this method clearly improves one-loop chiral perturbation theory, and a very good agreement between the inverse-amplitude method and the experimental information is obtained. This suggests that the inverse-amplitude method is a rather systematic way of improving chiral perturbation theory. ͓S0556-2821͑96͒02619-7͔