The oxygen-isotope record of palaeotemperature from Greenland ice cores has for many years been the kingpin of climate reconstructions for the North Atlantic region and northern Europe. An air temperature ‘seesaw’ between Greenland and northern Europe, first described in AD 1765, is also well known and is related to the North Atlantic Oscillation (NAO). Whereas the NAO index series is based on instrumental records of air pressure, the North Atlantic climate ‘seesaw’ has conventionally been based on air-temperature records. Here we describe relationships between this ‘seesaw’ mechanism and the Greenland (GISP2) oxygen-isotope chronology of air-temperature variations, as well as relationships between GISP2 Na+ (sea-salt) variations and instrumental records of North Atlantic storminess. The GISP2 proxy air-temperature record is calibrated for the last 130 years with instrumental weather records for West Greenland, while the Na+ series is compared with instrumental records of North Atlantic storminess change. Reconstruction of an annual series of these climate parameters for the last 1000 years shows that during the ‘Mediaeval Warm Period’ there were no years characterized by high Na+ extremes (high North Atlantic storminess) but there were many years when there were extremes of temperature. Remarkably, there were no years of exceptionally low air temperature and high Na+ precipitation at GISP2 between AD 1650 and 1710, a period of time that in northern Europe incorporates the period of maximum ‘Little Ice Age’ cooling. It would appear also that for the last thousand years the most extreme ‘seesaw’ winters when GISP2 temperatures were very low and Na+ concentrations were high occurred in discrete clusters and pairs of years.