We investigate defects in n-type ZnSe bulk crystals by positron annihilation. With positron lifetime spectroscopy, vacancies with a positron lifetime of (28061) and (275610) ps were found in ZnS:I and ZnSe:Al, respectively. The positron bulk lifetime was 241 ps at 300 K, determined in an undoped semi-insulating reference. The vacancies were identified to be Zn-vacancy donor complexes by combining the positron lifetime measurements with that of the positron-electron annihilation momentum distribution. This finding is supported by previous electron-paramagnetic-resonance measurements. The samples exhibited different degrees of electrical compensation, adjustable by thermal treatment under defined Zn vapor pressure. The vacancy concentration measured by positron annihilation could explain the deactivation of donors quantitatively. Thus, compensation of n-type conductivity in ZnSe is due to self-compensation through native Zn-vacancy donor complexes.