Do Cross-Sections Determine Phase Shifts Uniquely?

It is shown that scattering phase shifts are not uniquely determined by the differential cross-section. It can occur that two inequivalent sets of phase shifts correspond to exactly the same cross-section. The ambiguity is not limited to a finite number of nonvanishing phase shifts; a method is sketched for the generation of amplitudes with an exponentially decreasing tail of high partial-wave amplitudes.