  We analyze the perturbative Relativistic Moduli Space approach, where the
amplitudes of the Derrick modes are promoted to collective coordinates. In
particular, we analyse the possibility to calculate the critical velocity,
i.e., the initial velocity of kinks at which single bounce scattering changes
into a multi-bounce or annihilation collision, in the resulting Collective
Coordinate Model (CCM). We find that for a growing number of modes the critical
velocity of the CCM approaches the full field theory value. This is verified in
the case of the $\phi^4$ model, where we reach a $99\%$ accuracy. We also see
such a convergence for a wide range of models belonging to the family of the
double sine-Gordon and Christ-Lee theories, especially in those cases where the
kinks do not reveal a too well pronounced half-kink inner structure.
