The photoneutron cross sections for ${\mathrm{I}}^{127}$ and ${\mathrm{Pr}}^{141}$ have been measured with about 170- and 320-keV photon energy resolution, using monoenergetic photons obtained from annihilation in flight of positrons. The ($\ensuremath{\gamma}, n$), ($\ensuremath{\gamma}, 2n$), and ($\ensuremath{\gamma}, 3n$) cross sections were determined experimentally by a neutron-counting technique; hence, the nuclear photon-absorption cross sections were obtained without calculated multiplicity corrections. The photon-absorption cross section obtained for ${\mathrm{Pr}}^{141}$ is a single-peaked, giant dipole resonance, well described by a Lorentz-shaped curve with a maximum of 320 mb at 15.2 MeV and a width of 4.5 MeV. The ${\mathrm{I}}^{127}$ giant resonance is broadened slightly by its vibrational deformation. Although a single Lorentz curve is in fair agreement with the data, better agreement is obtained by the sum of two Lorentz curves, when adjusted to fit the data with the restrictions implied by the hydrodynamic model. The parameters of the two curves are: resonance energies, 15.2 and 15.8 MeV; peak cross sections, 180 and 50 mb; and widths, 4.1 and 8 MeV. The integrated nuclear photon-absorption cross sections of ${\mathrm{I}}^{127}$ and ${\mathrm{Pr}}^{141}$, obtained from the areas under the Lorentz curves which fit the data, are 1.8\ifmmode\pm\else\textpm\fi{}0.2 and 2.3\ifmmode\pm\else\textpm\fi{}0.2 MeV b, respectively. These integrated cross sections are in good agreement with the dipole sum rule uncorrected for exchange effects, which predicts 1.9 and 2.1 MeV b. The ${\mathrm{Pr}}^{141}(\ensuremath{\gamma}, 3n)$ threshold, which was measured to be 28\ifmmode\pm\else\textpm\fi{}1 MeV, determines the mass of ${\mathrm{Pr}}^{138}$.