Proton-proton partial-wave amplitudes for l>=1 and for lab kinetic energies below 350 MeV are fitted with a collection of single-particle exchanges taken in Born (fixed-pole) approximation. Since the Born terms are real, and consequently nonunitary, a correction term is added which makes the full amplitude unitary, and which at the same time satisfies the appropriate dispersion relation and threshold condition. The nature of this correction term and of its association with a strip approximation to the Mandelstam representation are discussed. The particle parameters were fitted to a reduced matrix representation of the p-p data, as described by Arndt and MacGregor in another publication. The S-wave dependence was removed in a manner also discussed by these authors. The gross structure of the partial-wave amplitudes is found to be approximately given by a sum of four meson-exchange poles, those corresponding to a π meson (JP=0-, I=1, gπ2=14, Mπ=135 MeV), a σ meson (JP=0+, I=0, gσ2=2.9, Mσ=450 MeV), an ω meson (JP=1-, I=0, gω2=4, (fg)ω=0, Mω=783 MeV), and a ρ meson (JP=1-, I=1, gρ2=1.2, (fg)ρ=4, Mρ=763 MeV). The searched parameters were gπ2, gσ2, gω2, gρ2, and Mσ the remaining parameters were fixed at their "physical" values. It is further found that the relatively small unitarizing corrections play an essential role in determining the goodness of fit, but they do not appreciably alter the pole parameters determined from the search. Studies were also undertaken to determine the manner in which this (obviously low-energy) model becomes quantitatively worse as low-angular-momentum and high-energy contributions are added to the calculation.