UHV-evaporated Ag1-xCux alloy films show a strong dependence of the crystallite sizes on the composition: In the middle of the concentration range, the mean grain size is smaller than 2 nm. The resistivity, however, is much lower than expected for such extremely-fine-grained materials (p < 9 my Omega cm). The electrical transport parameters for these films were obtained from the thickness dependence of the conductivity without any a priori assumptions. It will be shown that the electrical transport in these alloys can be well understood as a limit of the reflection model for the electrical conductivity in polycrystalline metals [G. Reiss, J. Vancea, and H. Hoffmann, Phys. Rev. Lett. 56, 2100 (1986)].