Taking advantage of the fact that the Vostok deuterium (deltaD) record now covers almost two entire climatic cycles, we have applied the orbital tuning approach to derive an age-depth relation for the Vostok ice core, which is consistent with the SPECMAP marine time scale. A second age-depth relation for Vostok was obtained by correlating the ice isotope content with estimates of sea surface temperature from Southern Ocean core MD 88-770. Both methods lead to a close correspondence between Vostok and MD 88-770 time series. However, the coherence between the correlated deltaD and insolation is much lower than between the orbitally tuned deltaD and insolation. This reflects the lower accuracy of the correlation method with respect to direct orbital tuning. We compared the ice and marine records, set in a common temporal framework, in the time and frequency domains. Our results indicate that changes in the Antarctic air temperature quite clearly lead variations in global ice volume in the obliquity and precession frequency bands. Moreover, the average phase we estimated between the filtered deltaD and insolation signals at precessional frequencies indicates that variations in the southern high latitude surface temperature could be induced by changes in insolation taking place during a large period of the summer in northern low latitudes or winter in southern low latitudes. The relatively large lag found between Vostok deltaD variations and obliquity-driven changes in insolation suggests that variations in the local radiative balance are not the only mechanism responsible for the variability in surface temperature at those frequencies. Finally, in contrast to the cross-spectral analysis method used in previous studies, the method we use here to estimate the phases can reveal errors in cross-correlations with orbitally tuned chronologies.