The universality of the frequency-dependent ͑AC͒ conduction of many disordered solids in the extremedisorder limit has been demonstrated experimentally. Theoretically, this universality has been established with different techniques and for various models. A popular model that has been extensively investigated and for which AC universality was established is the symmetric random-barrier model without Fermi statistics. However, for the more realistic model of random site-energies and Fermi

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... tics AC universality has never been rigorously established. In the present work we perform a numerical study of the latter model for a regular lattice in two dimensions. In addition, we allow for variable-range hopping. Our main conclusion is that AC universality appears to hold for this realistic model. The obtained master curve for the conductivity and the one obtained for the random-barrier model in two dimensions appear to be the same.