Accurate prediction of motion extremes for moored floating offshore structures remains a subject of considerable interest to the offshore industry. The difficulty of predicting extremes lies in the method used to combine motions at the incident wave and slow-drift frequency scales. Since vessel excursions are dependent on both intensity and frequency composition of the incident wave field, the critical design case is unclear and hence accurate, efficient frequency domain analysis tools are becoming essential to preliminary design. Frequency domain extreme prediction methods may be broadly categorised as either empirical combination, such as those used in the current design codes and rules of recommended practice, or rigorous statistical methods which are based on predicting crossing rates and applying a 'correction' factor for the potential clumping of wave peaks. For the latter class of method, rapid, prediction of the mean up-crossing rates is essential. This article compares various published methods for predicting crossing rates using the Faltinsen and Loken floating cylinder in irregular beam seas data. By comparison with methods of high computational intensity, it is shown that lower order methods are able to efficiently and accurately predict crossing rates and the associated (uncorrected) motion extremes. (C) 2003 Elsevier Ltd. All rights reserved.