Drill sites recovered from the South Atlantic by the Deep Sea Drilling Project provide excellent magnetostratigraphies for the time-interval of polarity chrons C33r through C28n (83-62.5 Ma: Cande & Kent time-scale). Cyclic patterns of carbonate sedimentation, with a mean repeat time of ca. 20 ka, can be correlated between sites. The cycles show the full hierarchy of eccentricity amplitude modulations that would be expected of precessional orbital forcing. A significant modulations that would be expected of precessional orbital forcing. A significant modulation component exists at ca. 400 ka, which in all likelihood matches the modern 404 ka repeat time for eccentricity. This modulation pattern may provide the "tuning fork" for tying cyclical sedimentation to the most stable astronomical eccentricity period. A ca. 2.5 Ma modulation also emerges that seems surprisingly similar to the modern long-wavelength eccentricity modulation of precessional amplitude, which should average 2.425 Ma. Results of "cyclochronology" of polarity chrons C29n-C31n suggest that the Cande & Kent time-scale will need to be revised to allow for a more gentle change in South Atlantic sea-floor spreading than modelled by those authors.