We calculate the contribution of recently found, highly inelastic πN resonances in the S31, S11, P11, and D13 partial waves to the exchange u-channel generalized potential for πN scattering. We use the results of the complex phase-shift analyses for incident pion energies <=1 BeV joined to smooth asymptotic functions to obtain the absorptive parts of the amplitudes. Dispersion integrals are performed over these amplitudes in the physical u region and then related to the direct s channel by crossing. Finally, partial-wave projections in the direct s channel give the partial-wave generalized-exchange u-channel potential input to the ND equations, which are solved for the phase shifts in the direct channel. The results are as follows: (i) Compared to the exchange of the nucleon and the N*33 (1238 MeV), the S11, S31, and P11 u-channel continua have relatively small contributions to the s-channel unphysical cut. (ii) As for the P33 partial wave, the D13 contribution to the u-channel exchange potential is divergent at large s. Thus a cutoff is needed to solve the ND equations. The effect of including D13 exchange is to make it harder to obtain agreement with experiment. (iii) The detailed shape of the P33 resonance reduces its contribution to the exchange potential by a factor of 0.75 as compared with the narrow-width approximation.