  In previous works, ratios among four-point scattering amplitudes at the
leading order in the high-energy limit were derived for the bosonic open string
theory. The derivation was based on Ward identities derived from the decoupling
of zero-norm states and was purely algebraic. The only assumption of the
derivation was that the momentum polarization can be approximated by the
longitudinal polarization at high energies. In this paper, using the decoupling
of spurious states, we reduce this assumption to a much weaker one which can be
easily verified by simple power counting in most cases. For the special cases
which are less obvious, we verify the new assumption for an example by
saddle-point approximation. We also provide a new perspective to our previous
results in terms of DDF states. In particular, we show that, by using DDF
states, one can easily see that there is only one independent high energy
scattering amplitude for each fixed mass level.
