Partial wave amplitudes have been extracted from accurate data on pbar + p ->
pi + pi by a method which incorporates the theoretical constraints of
analyticity and crossing symmetry. The resulting solution gives a good fit to
the annihilation data and is also consistent with the wealth of information in
the crossed channel pi + N -> pi + N. The partial wave amplitudes show evidence
for resonances in all partial waves with J < 6, at least one of which, a J = 0+
state, (and possibly another with J = 1-) is unlikely to have a simple
quark-antiquark structure.Comment: 17 pages, Revtex, 21 postscript figure