The late Pliocene-early Pleistocene sapropel-bearing sequences exposed in the Vrica, Semaforo, Singa and Punta Piccola sections of southern Italy and the Francocastello section on Crete have been calibrated to the new astronomical solutions for the precession of the equinox and the eccentricity of the Earth's orbit using inferred phase relationships between these orbital cycles and the sapropel cycles. A new Mediterranean Precession-Related Sapropel (MPRS) coding is introduced according to which sapropels are coded after the correlative peak of the precession index as numbered from the Recent. These sapropels can now be dated with an accuracy of 1 ka by taking a time lag of 4 ka between orbital forcing, and maximum climate response and sapropel formation into account. This tuning further results in ages for the Pliocene-Pleistocene boundary (1.81 Ma), the top of the Olduvai (1.79 or 1.84), the bottom of the Olduvai (1.95 +/- 0.01), the Reunion (2.14-2.15), the Gauss/Matuyama (2.59/2.62) and the top of the Kaena (3.02 +/- 0.01). These ages are remarkably similar to the astronomically calibrated ages obtained independently by Shackleton et al. based on ODP Site 677 ([1], Trans. R. Soc. Edinb., 81, 1990), but deviate considerably from those provided by Ruddiman et al. ([2], Paleoceanography, Vol. 4) and Raymo et al. based on DSDP Site 607 ([3], Paleoceanography, Vol. 4). The constant discrepancy of 130 ka with the time scale of Ruddiman et al. and Raymo et al. is explained by the new age of 0.78 instead of 0.73 Ma for the Brunhes/Matuyama, as recently proposed by Shackleton et al., and the fact that Ruddiman et al. missed two obliquity related cycles in the Brunhes/Matuyama to top Olduvai interval. Our astronomically calibrated ages do not confirm the conventional radiometric ages of the reversal boundaries, but, on the contrary, imply that K/Ar radiometric dating yields ages that are consistently too young by 5-7%.