The large, abrupt, widespread, millennial changes recorded in many paleoclimatic archives pose a major challenge to our understanding of the climate system. Both periodic and stochastic models have been proposed to explain these events. We have argued that Greenland ice-core data are more consistent with a stochastic-resonance hypothesis. In this model, a combination of a weak periodicity plus "noise" perhaps caused by ice-sheet-related changes in freshwater flux to the north Atlantic produced switches between warm and cold climate modes. Here, we show that the stochastic-resonance hypothesis is consistent with a wider range of previously published data than analyzed before including a north Atlantic marine record and the Byrd Station, Antarctica iceisotopic record; however, a record of hematite-stained quartz grains in north Atlantic sediment appears more periodic than stochastically resonant.