The A1−ρ−π system is studied and it is shown that the question of possible subtractions in the dispersion relations for form factors is crucial for understanding the difference between hard- and soft-pion results in the A1 and ρ decays. A double dispersion representation is suggested for three-point functions. Using a truncation approximation, the Bjorken technique is employed to derive several new sum rules for the spectral functions. Assuming that the sum rules are saturated by low-lying meson states, a study is made to evaluate the constant terms in the dispersion representations of the form factors involved in the A1ρπ and ρππ vertices. The case of no subtractions, which formally leads to the soft-pion results, is ruled out on the basis of this investigation, and the well-known hard-pion results for A1 and ρ decays are rederived.