We present an atomic-structure model for high-quality AlCuFe icosahedral quasicrystals which is simple and yet incorporates most of what is known about the microscopic structure of the AlCuFe alloy. Using realistic image simulations, we compare this model with actual lattice-image micrographs of thermodynamically stable quasicrystal. We find good agreement between the micrographs and the models, although we find that lattice imaging is incapable of distinguishing small differences in the atomic structure. We have also determined the microscope defocus conditions that produce the most faithful images. © 1993.