First-principles calculations on p-type doping of the paradigm wide-gap ZnO semiconductor reveal that successful doping depends much on engineering a stable local chemical bonding environment. We suggest a cluster-doping approach in which a locally stable chemical environment is realized by using few dopant species. We explain two puzzling experimental observations, i.e., that monodoping N in ZnO via N2 fails to produce p-type behavior, whereas using an NO source produces metastable p-type behavior, which disappears over time.