  We consider the problem of recovering a smooth, compactly supported potential
on R^3 from its backscattering data. We show that if two such potentials have
the same backscattering data and the difference of the two potentials has
controlled angular derivatives then the two potentials are identical. In
particular, if two potentials differ by a finite linear combination of
spherical harmonics with radial coefficinets and have the same backscattering
data then the two potentials are identical.
