Crossing-symmetric solutions to the pion-pion partial-wave dispersion relations are obtained, using the inverse-amplitude method. The presence of the ρ meson with its physical mass and width is assumed, the amplitudes are constrained to contain Adler zeros, and general sum rules and inequalities are satisfied. Favored solutions contain a very broad isoscalar S-wave resonance, and have a small decreasing isospin-2 S-wave phase shift. The D waves are very small. The over-all agreement with phenomenology and with other S-matrix calculations is very good.