A method of statistical testing of analyticity is applied to pion-pion phase shifts in order to obtain the pole positions in the second sheet of the complex energy plane for the resonances in the S, P , and D partial waves. Whereas the positions of the dominant resonances are found at mp = (768 i.4) -i ( 7 4 k 3) MeV, m,. = (998 & 7) -i(19 f 6) MeV, and ml = (1268 + 34) -i(94 25) MeV, no conclusions about the ~(1300) or the ~'(1600) could be reached.