We present calculations on reactions of the type X + CZ(3)Y --> XY + CZ(3) using a reduced-dimensionality model with two degrees of freedom. Only the Y-C vibrational mode vi Of CZ3Y and the stretching vibration of X-Y are treated explicitly in the scattering problem. An approximation accounting for the umbrella nu(2) mode of CZ(3) has been introduced. A direct comparison with previous calculations of state-selected reaction cross sections is made on the reactions O(P-3) + CH4 --> OH + CH3 and O(P-3) + CH3D --> OD + CH3. The results show that the approximation applied, in which the umbrella mode is not accounted for explicitly in the scattering calculations, gives good results for some vibrationally selected reaction cross sections. In agreement with previous results, we find that the umbrella mode is more efficient in promoting the O(P-3) + CH4 --> OH + CH3 reaction and that the stretching vibration enhances the O(P-3) + CH3D --> OD + CH3 reaction.