We apply two-step phenomenology (S(l) fit then inversion) to establish
local potentials fitting the elastic scattering of Li-11 from Si-28 a
t 319 MeV lab energy and Li-11 from C-12 at 637 MeV lab energy. We rea
dily find potentials giving goad fits. Despite severe ambiguity proble
ms, a consistent picture emerges which in essential features is common
to both cases. Potentials are found which entail a much longer tail o
n the real component than is predicted by folding models which incorpo
rate current models of halo structure. We suggest a picture of Li-11 s
cattering in which the two outer neutrons contribute to a long tail in
the real part of the potential, but not in the imaginary part.