The correct form of radiation conditions is found in scattering problem for threeparticle Hamiltonians $H$. For example, in a cone $\Gamma$ of the configuration space where all pair potentials are vanishing the radiation conditions-estimate has the following form. Let $\nabla ^{(s)}$, $\nabla ^{(s)}u(x) = \nabla u(x) - |x|^{-2} \langle \nabla u(x),x \rangle x,$ be the projection of the gradient $\nabla$ on the plane, orthogonal to $x$, and let $\xi$ be the characteristic function of $\Gamma$. Then the operator $\xi (|x| + 1)^{-1/2}\nabla ^{(s)}$ is locally (away from thresholds and eigenvalues of $H$) $H$-smooth (in the sense of T.Kato). In cones where some of pair potentials are not vanishing radiation conditions-estimates have similar (though weaker) form with the gradient replaced by its projection on a certain subspace. Such estimates allows us to give an elementary proof of the asymptotic completeness for three-particle systems in the framework of the theory of smooth perturbations.