A particular modification of the free-field representation of the form factors in the Bullough-Dodd model is considered. The two-particles minimal form factors are excluded from the construction. As a consequence, a convenient representation for the multiparticle form factors has been obtained, recurrence relations between them have been established, and their properties have been studied. The proposed construction is used to obtain the free-field representation of the lightest particles form factors in the Φ _{1, 2} perturbed minimal models. The Ising model in a magnetic field is considered as a significant example. The results obtained in the framework of the proposed free-field representation are in agreement with the corresponding results obtained by solving the bootstrap equations.