Abrupt climate change is a ubiquitous feature of the Late Pleistocene epoch. In particular, the sequence of Dansgaard-Oeschger events (repeated transitions between warm interstadial and cold stadial conditions), as recorded by ice cores in Greenland, are thought to be linked to changes in the mode of overturning circulation in the Atlantic Ocean. Moreover, the observed correspondence between North Atlantic cold events and increased iceberg calving and dispersal from ice sheets surrounding the North Atlantic has inspired many ocean and climate modelling studies that make use of freshwater forcing scenarios to simulate abrupt change across the North Atlantic region and beyond. On the other hand, previous studies identified an apparent lag between North Atlantic cooling events and the appearance of ice-rafted debris over the last glacial cycle, leading to the hypothesis that iceberg discharge may be a consequence of stadial conditions rather than the cause. Here we further establish this relationship and demonstrate a systematic delay between pronounced surface cooling and the arrival of ice-rafted debris at a site southwest of Iceland over the past four glacial cycles, implying that in general icebergs arrived too late to have triggered cooling. Instead we suggest that - on the basis of our comparisons of ice-rafted debris and polar planktonic foraminifera - abrupt transitions to stadial conditions should be considered as a nonlinear response to more gradual cooling across the North Atlantic. Although the freshwater derived from melting icebergs may provide a positive feedback for enhancing and or prolonging stadial conditions, it does not trigger northern stadial events.