There was a significant oxidation of the Earth's surface around 2 billion years ago (2 Gyr). Direct evidence for this oxidation comes, mostly, from geological records of the redox-sensitive elements Fe and U reflecting the conditions prevailing during weathering. The oxidation event was probably driven by an increased input of oxygen to the atmosphere arising from an increased sedimentary burial of organic matter between 2.3 and 2.0Gyr. This episode was postdated by the final large precipitation of banded iron formations around 1.8Gyr. It is generally believed that banded iron formations precipitated from an ocean whose bottom waters contained significant concentrations of dissolved ferrous iron, and that this sedimentation process terminated when aerobic bottom waters developed, oxidizing the iron and thus removing it from solution. In contrast, I argue here that anoxic bottom waters probably persisted until well after the deposition of banded iron formations ceased; I also propose that sulphide, rather than oxygen, was responsible for removing iron from deep ocean water. The sulphur-isotope record supports this hypothesis as it indicates increasing concentrations of oceanic sulphate, starting around 2.3Gyr, leading to increasing rates of sulphide production by sulphate reduction. The increase in sulphide production became sufficient, around 1.8Gyr, to precipitate the total flux of iron into the oceans. I suggest that aerobic deep-ocean waters did not develop until the Neoproterozoic era (1.0 to ~0.54Gyr), in association with a second large oxidation of the Earth's surface. This new model is consistent with the emerging view of Precambrian sulphur geochemistry and the chemical events leading to the evolution of animals, and it is fully testable by detailed geochemical analyses of preserved deep-water marine sediments.