The most reliable technique for predicting the statistical properties of the response of an offshore structure to random wave loading is the time simulation technique. However, this technique requires very long simulations in order to reduce the sampling variability to acceptable levels. If this technique can be speeded up, then it would be an ideal technique because it does not suffer from any of the inadequacies of the alternative methods and is applicable to all different types of structures. To this end, a more efficient version of the time simulation technique (ETS) has been introduced which divides the simulated response extreme values into a number of groups based on the magnitude of the extreme values of their associated surface elevation or linear response records. The probability distribution of extreme responses for each group is then calculated individually based on a relatively small number of simulations. Finally, the total probability theorem is used to derive the probability distribution of response extreme values. The ETS procedure is found to be many times more efficient than the conventional method.