Recent analysis of 38 globally distributed paleoclimatic records covering Marine Isotope Stage 3 (MIS 3) 60–26 ka demonstrated that the two leading empirical orthogonal functions (EOFs) explaining the data are the Greenland ice-core signal (“northern” signal) and the Antarctic ice-core signal (“southern” signal). Here singular spectral analysis (SSA) is used to show that millennial-scale variability of each of these two leading EOFs is characterized by two independent modes. The two modes of each EOF share similar relative distributions of variance, identical spectra, and, where each mode has spectral power, coherency spectra, which are significantly above the null hypothesis level at 95% confidence. The only difference between the modes of the northern and southern signals is that they are phase shifted. The phasing and long response time of the low-frequency mode, combined with its relationship to atmospheric CO2 and sea level, are consistent with coupled changes in the ocean, ice sheets, atmosphere, and carbon cycle, whereas the phasing and short response time of the high-frequency mode are consistent with an atmospheric transmission likely induced by changes in hemispheric sea ice distributions and attendant feedbacks.