High-quality Bi2Sr2CaCu2O8+ superconducting single crystals, annealed at different oxygen partial pressures, have been studied using angular-resolved x-ray photoelectron spectroscopy with a resolution higher than that used in any previous study. Two states of the oxygen, separated by 0.7 eV, are unambiguously observed. Examining these components at different angles makes it possible to distinguish bulk from surface components. Using this capability we discover that annealing under lower oxygen partial pressure (1 atm) results in oxygen intercalation beneath the Bi-O surface layer of the crystal, whereas for higher-pressure anneals (12 atm) additional oxygen is found on the Bi-O surfaces. This steplike intercalation mechanism is also confirmed by the changes observed in the Cu and Bi core lines as a function of the annealing oxygen partial pressure. © 1991 The American Physical Society.