A remarkable increase of the silver conductivity in glassy ${\mathrm{AgPO}}_{3}$ by four orders of magnitude is known to occur on adding ${\mathrm{PbI}}_{2}.$ We have investigated the structural changes that occur on ${\mathrm{PbI}}_{2}$ doping in $({\mathrm{PbI}}_{2}{)}_{0.1}{\ensuremath{-}(\mathrm{A}\mathrm{g}\mathrm{P}\mathrm{O}}_{3}{)}_{0.9}$ and $({\mathrm{PbI}}_{2}{)}_{0.1}{\ensuremath{-}(\mathrm{AgI})}_{0.1}{\ensuremath{-}(\mathrm{A}\mathrm{g}\mathrm{P}\mathrm{O}}_{3}{)}_{0.8}$ using neutron- and x-ray-diffraction and Raman-scattering experiments. The microscopic structure of the glasses were modeled using the reverse Monte Carlo method, which produced structural models that are in quantitative agreement with both the x-ray and the neutron data, as well as with the experimental density and applied physical constraints on P-O coordination number and closest atom-atom approach distances. The aim was to examine the structural role of the immobile ${\mathrm{Pb}}^{2+}$ and ${\mathrm{I}}^{\mathrm{\ensuremath{-}}}$ ions for the ionic conductivity. The results show that the ${\mathrm{Pb}}^{2+}$ and ${\mathrm{I}}^{\mathrm{\ensuremath{-}}}$ ions expand the ${\mathrm{PO}}_{4}$ network, which opens doorways and creates new pathways in the structure suitable for ion conduction. Furthermore, almost all the ${\mathrm{Pb}}^{2+}$ ions coordinate mainly to oxygens and in that way contribute to a partial dissociation of the ${\mathrm{Ag}}^{+}$ ions from the nonbridging oxygens. The iodine ions play a similar role by expanding the host glass and coordinating to silver ions, leading to a further decrease of the Ag-O coordination. The ${\mathrm{PbI}}_{2}$-induced expansion of the glass network and reduction of the average Ag-O coordination number are likely to decrease both the elastic strain energy ${E}_{g}$ and the electrostatic binding energy ${E}_{b}$ and thereby the total activation energy for ${\mathrm{Ag}}^{+}$ migration.