The effect of pressure on the ionic conductivity of Rb${\mathrm{Ag}}_{4}$${\mathrm{I}}_{5}$ and AgI has been measured, using single crystals and polycrystalline samples, up to pressures of 6 kbar. The activation volumes for motion in $\ensuremath{\alpha}\ensuremath{-}\mathrm{Rb}{\mathrm{Ag}}_{4}{\mathrm{I}}_{5}$ and $\ensuremath{\beta}\ensuremath{-}\mathrm{Rb}{\mathrm{Ag}}_{4}{\mathrm{I}}_{5}$, respectively, are -0.4 \ifmmode\pm\else\textpm\fi{} 0.2 and -0.2 \ifmmode\pm\else\textpm\fi{} 0.1 ${\mathrm{cm}}^{3}$/mole. In $\ensuremath{\alpha}\ensuremath{-}\mathrm{AgI}$, the motion volume increases from 0.56 \ifmmode\pm\else\textpm\fi{} 0.1 ${\mathrm{cm}}^{3}$/mole at 435 K to 0.8 \ifmmode\pm\else\textpm\fi{} 0.1 ${\mathrm{cm}}^{3}$/mole at 623 K. These values are unusually small in relation to the activation energies and are not consistent with the strain-energy model or a domain-diffusion mechanism. The logarithms of the ionic conductivities of $\ensuremath{\alpha}$- and $\ensuremath{\beta}\ensuremath{-}\mathrm{Rb}{\mathrm{Ag}}_{4}{\mathrm{I}}_{5}$ increase linearly at first and then decrease quadratically with pressure. This is related to the large quadratic pressure dependence of the second-order transition temperature $\ensuremath{\Delta}{T}_{c}(\mathrm{K})=0.141P(\mathrm{kbar})+0.111{P}^{2}({\mathrm{kbar}}^{2})$. The variation of the 122-K transition temperature with pressure is $\ensuremath{\Delta}{T}_{c}(\mathrm{K})=5.65P(\mathrm{kbar})\ensuremath{-}0.53{P}^{2}({\mathrm{kbar}}^{2})$, implying a molar volume change of ${V}_{\ensuremath{\beta}}\ensuremath{-}{V}_{\ensuremath{\gamma}}=0.37\ifmmode\pm\else\textpm\fi{}0.01$ ${\mathrm{cm}}^{3}$/mole and a change in compressibility ${K}_{\ensuremath{\beta}}\ensuremath{-}{K}_{\ensuremath{\gamma}}=(0.033\ifmmode\pm\else\textpm\fi{}0.001)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ ${\mathrm{cm}}^{2}$/dyn across the transition. The ionic conductivity of $\ensuremath{\gamma}\ensuremath{-}\mathrm{Rb}{\mathrm{Ag}}_{4}{\mathrm{I}}_{5}$ initially decreases with an activation volume of 9 \ifmmode\pm\else\textpm\fi{} 1 ${\mathrm{cm}}^{3}$/mole, and then levels off with increasing pressure. The negative activation volume for conduction along the $c$ axis in $\ensuremath{\beta}\ensuremath{-}\mathrm{AgI}$ has been confirmed. Both low-temperature phases have large formation volumes consistent with the theory of Rice et al. of transitions to the superionic phase.