Extreme waves are an important ocean feature. We estimate return values of significant wave height from measurements by satellite altimeters over the North Atlantic. The data were divided into 2 degrees latitude by 2 degrees longitude grid squares and the median along the satellite track was taken in each. Return values were estimated by fitting a Generalised Pareto Distribution to all values above a threshold, which was allowed to vary spatially. This method is objective, more statistically robust and thus theoretically preferable to fitting a distribution to all the data. The novel method gave return values that were up to 37% smaller than those estimated by fitting a Fisher-Tippet 1 distribution to all the data. (c) 2005 Elsevier Ltd. All rights reserved.