We determine the spectrum and the factorizable S-matrices of the massive excitations of the non-unitary minimal models M 2,2n + 1 perturbed by the operator ø 1,2. These models present no kinks as asymptotic states, as follows from the reduction of the Zhiber-Mikhailov-Shabat model with respect to the quantum group SL(2) q found by Smirnov. We also give the whole set of S-matrices of the non-unitary minimal model M 2,9 perturbed by the operator ø 1,4, which is related to a RSOS reduction for the ø 1,2 operator of the unitary model M 8,9. The thermodynamical Bethe ansatz and the truncated conformal space approach are applied to these scattering theories in order to support their interpretation.