The shallow donor impurities in ZnO with binding energies between 46 and 56 meV have been studied in great detail in the recent years. They give rise to neutral donor bound exciton recombinations with the A- and B-valence bands, show rotator states and two-electron-satellite transitions. These properties allowed to establish the excited state splittings of the donors as well as confirming Hayne's rule in ZnO. So far they all seem to be of extrinsic origin, hydrogen, aluminum, gallium and indium in order of increasing binding energy. For many years it was common sense that intrinsic defects would dominate the n-type conductivity of ZnO. Interstitial zinc as well as oxygen vacancies should be double donors, and in order to contribute to the n-type-conduction they should have shallow levels, and low formation energies to be abundant. In PL-measurements at T∼100 K on various ZnO samples, single crystals as well as thin films, a luminescence around 3.31 eV was detected. Due to its line shape and temperature behaviour it is identified as bound-to-free recombination. If we assume that the 3.31 eV band with its level at EC ∼ 130 meV is the ++/+ level of the zinc interstitial we calculate for the binding energy of the +/0 level ∼ 130 meV, i.e. around 33 meV. Undoped Zn-rich epitaxial films grown by CVD show a dominant I3 recombination at 3.367 eV which according to Haynes rule is consistent with a shallow donor level at 33 meV. Moreover, they have free n-type carrier densities of 2×1019 cm−3 and as revealed by SIMS the common donor impurities (Al, Ga, In) cannot account for the high carrier densities.