We consider a certain modification of the free-field representation of the form factors in the Bullough-Dodd model. The two-particle minimal form factors are eliminated from the construction. We consequently obtain a convenient representation for the multiparticle form factors, establish recurrence relations between them, and study their properties. We use the proposed construction to obtain the free-field representation of form factors for the lightest particles in the Φ_1,2-perturbed minimal models. As an important example, we consider the Ising model in a magnetic field. We verify that the results obtained in the framework of the proposed free-field representation agree with the corresponding results obtained by solving the bootstrap equations.