The left-hand discontinuities in the partial-wave amplitudes for π-π scattering are assumed to be dominated by the exchange of the ρ meson in a form suggested by the Regge representation for a resonance. This Regge behavior provides the necessary high-energy cutoff and allows the ND equations to be solved. The partial-wave I=1 amplitudes are calculated for noninteger angular momenta l<1 as well as l=1. The trajectory αρ(s) as well as the residue βρ(s) of the ρ-meson Regge pole are evaluated. An attempt is made to obtain a self-consistent solution for the relevant parameters, namely the position and width of the ρ resonance and αρ(0). The results of this calculation give αρ(0)>~0.9. The I=0 vacuum trajectory is also discussed.