The exceedance probability of wave crest elevation is a critical environmental input for the design/re-assessment of marine structures. With attention often focused on structural reliability, and in some cases survivability, the largest wave crests arising at the smallest exceedance probabilities, said to be located in the tail of a distribution, are of primary interest. This paper explains why present design practice may be non-conservative in the most extreme seas and outlines a new method by which the tail of the distribution can be defined using a relatively small number of deterministic wave events. This avoids the need to explore the entire distribution using very long (and expensive) random wave simulations. The new approach allows both an extension of the distribution to smaller exceedance probabilities and a concentration on the largest most design relevant crest heights. Having demonstrated the success of the proposed method by comparisons to laboratory data, the analysis is extended to include the effective prediction of the associated confidence intervals (CIs). With the highest waves subject to the largest statistical uncertainty, the paper explores the nonlinear changes in CI, demonstrates that these can also be accurately and efficiently defined, and explains how CI may be reduced. The focus of the paper lies in improved design calculations, based upon the nonlinear dynamics of extreme waves in realistic seas.