Millennial-scale climate oscillations of the last ice age registered in Greenland and Antarctic ice cores did not always vary in unison. A striking example is that the strongest Antarctic warming episodes occurred during Heinrich episodes in the North Atlantic region. Although the bipolar seesaw affords a possible explanation for such anti-phasing, it does not account for the equally striking observation that climate varied in unison between the hemispheres about half the time. Such phasing differences suggest the need for an alternative hypothesis in which the polar regions at times responded in unison to common forcing, and at other times left the impression of a bipolar seesaw. We posit that this impression arose from the effect of warmer-than-usual summers on continental ice sheets adjacent to the North Atlantic Ocean during each Heinrich episode. The relatively warm Heinrich summers produced discharges of meltwater and icebergs of sufficient volume to stimulate very cold winter conditions from widespread sea ice on a freshened ocean surface. The intervals between Heinrich episodes featured relaxation of sea-ice-induced winter severity from reduced summertime influx of meltwater and icebergs, indicating relatively cooler summer conditions. It is postulated that the causative variations in freshwater fluxes were driven by a climate signal most evident in Antarctic ice cores but also recognized in other paleoclimate records in both polar hemispheres. We suggest that this widespread signal arose from changes in the latitude and strength of the austral westerlies and the resulting effect on the western Pacific tropical warm pool, a mechanism dubbed the Zealandia Switch.