The dynamic behavior of structures in the offshore environment is complex, especially in extreme storm conditions. The most accurate methods for estimating structural behavior are based on extensive random time domain simulations of the ocean surface to obtain statistics of the extreme response in (typically) a 3 hour period of a severe storm. However, random time domain simulation is time-consuming and expensive for both the computer and the engineer. In this work the authors use a method to determine the distribution of the extreme structural response in a robust, faster and cheaper way than with full random simulations. This method, which is based on constrained random simulations, has been successfully developed using a grossly simplified model of a jack-up. The aim of this study is now to include more realistic modelling parameters in order to demonstrate that the method can be successfully applied to real problems and that accurate results can be obtained with relatively little effort.