Zn-and O-isotopically enriched ZnO nanorods were grown with excellent optical quality allowing an identification and resolution of various bound exciton zero phonon lines. Furthermore, the well-known Cu-related emission at 2.86 eV could specifically be studied in order to investigate the local environment of the defect including possible involvement of native defects such as interstitials and vacancies in this deep centre. Energetic shifts of this zero phonon line were measured and compared to changes in the near band edge energies as a function of the enrichment. No relative shift was observed in Zn-enriched samples, indicating that only O atoms lie in the immediate vicinity of the Cu atom, and that Zn interstitials and O