The mooring design of a floating offshore structure requires the estimation of mooring responses corresponding to annual exceedance probabilities of 10−2 (extreme event) and sometimes 10−4 (survival event). The most straightforward method to determine the extreme design response under a specified design sea state, is to carry out N time domain simulations, so as to capture the inherent randomness of this sea state and use the N maximum values to estimate the most probable maximum response for design. However, this requires typically 30–40 time-domain analyses of the same design sea state, which is computationally extensive. In this paper it is shown that the required number of time domain simulations can be reduced significantly by utilising the peaks of the mooring tension time series, obtained from time domain simulations, to derive a distribution for the maxima. Different variations of using these peaks are explored and a “best practice” for this technique is proposed. In order to establish a robust benchmark for evaluating and validating this “best practice”, extensive time domain simulations have been carried out for a large permanently connected, weathervaning vessel, with catenary mooring system, in a tropical cyclone environment. Both extreme and survival conditions are explored, by running 170 3-h simulations for each condition, thereby representing in detail the random nature of each sea state. It is shown that a reliable distribution for the maxima, (within ±4% from the benchmark) can be obtained in a manner which is simple and computationally efficient, based on just 4–7 time domain analyses. Thus by using more peaks from the time domain analyses, there is a significant gain in terms of accuracy and efficiency. The above “best practice” is used to calculate the most probable maximum mooring line response and the variability of this maximum (short term variability) within a 3-h sea state for environmental conditions with annual exceedance probabilities of 10−2 and 10−4. It is shown that the short term variability is not invariant but may be described in terms of a Gumbel distribution whose parameters depend on the magnitude of the response. These expressions provide a means of calculating the long term distribution of mooring line load, accounting for the short term variability, which can be used to address the reliability of a mooring system.