The purpose of this paper is to derive three new random seaway models that appear to have some properties of actual seas not illustrated by previous models, to derive a few of these properties and discuss other possible properties, and to show how these models appear to be more realistic by comparing them with selected observations. These new models explain some of the difficulties that arise with the higher spectral moments. They may also be capable of giving some information about whitecaps, breaking waves, and sharp crested waves. Since all mathematical models of nature fail in one way or the other when the conditions and assumptions in the derivation are not met, these models will provide a second choice when observations of waves are to be compared with theoretical results. Some questions are raised that can only be answered by additional theoretical work and by precise measurements of waves.