Abrupt, switch-like, changes in sea ice cover are proposed as a mechanism for the large-amplitude abrupt warming that seemed to have occurred after each Heinrich event. Sea ice changes are also used to explain the colder-than-ambient glacial conditions around the time of the glacier discharge. The abrupt warming events occur in this mechanism, owing to rapid sea ice melting which warmed the atmosphere via the strong sea ice albedo and insulating feedbacks. Such abrupt sea ice changes can also account for the warming observed during Dansgaard-Oeschger events. The sea ice changes are caused by a weak (order of 5 Sv) response of the thermohaline circulation (THC) to glacier discharges. The main point of this work is therefore that sea ice may be thought of as a very effective amplifier of a weak THC variability, explaining the abrupt temperature changes over Greenland. Synchronous ice sheet collapses from different ice sheets around the North Atlantic, indicated by some proxy records, are shown to be possible via the weak coupling between the different ice sheets by the atmospheric temperature changes caused by the sea ice changes. This weak coupling can lead to a nonlinear phase locking of the different ice sheets which therefore discharge synchronously. It is shown that the phase locking may also lead to precursor glacier discharge events from smaller ice sheets before the Laurentide Ice Sheet discharges. The precursor events in this mechanism are the result rather than the cause of the major glacier discharges from the Laurentide Ice Sheet.