Diffusion experiments of N, Li, and Na into single-crystal substrates of ZnO were performed. The diffused layers were studied using mass spectroscopy and low temperature photoluminescence. Based on earlier investigations Li and Na produce deep acceptor states which participate in shallow donor to deep acceptor recombinations in the visible spectral region. We will demonstrate that in the case of group-I elements also shallow acceptors are introduced having binding energies around 300 meV. The corresponding donor–acceptor pair recombinations have weak electron–phonon coupling analogous to the “edge” emissions in other II-VI compounds. With 160 meV nitrogen so far has the smallest ionisation energy. We compare our results with ZnO epitaxial films where the respective elements are incorporated during growth.