  The question is discussed: to what extent the often assumed independence of
the phase of the elastic scattering amplitude from the momentum transfer
\textit{in the region of only small values} of $ t $ limits $ t $-dependence of
the phase generally. Analyticity allows to give a proof that if the phase of a
strong interaction scattering amplitude is independent on the transferred
momentum $ t $ at small values of $ t $ then it does so in all physical region.
Moreover, if such an independence holds in any physical energy $ \sqrt{s} $
region including the values infinitesimally close to the first inelastic
threshold from below the whole scattering amplitude vanishes. Relationship of
the $ t $-dependence of the phase with the size of the interaction range is
also discussed.
